Understanding basic motion calculations in games: Euler vs. Verlet

During the past month, I have found myself in the position of having to explain the contents of this article to six different persons, either at work or over the Internet. Though there are a lot of articles on the subject, it’s still as if almost everyone gets it wrong. I was still polishing this article when I had the opportunity to explain it a seventh time.

And two days ago a coworker told me the source code of a certain framework disagreed with me… The kind of framework that probably has three NDAs preventing me from even thinking about it.

Well that framework got it wrong, too. So now I’m mad at the entire world for no rational reason other than the ever occurring realisation of the amount of wrong out there, and this article is but a catharsis to deal with my uncontrollable rage.

A simple example

Imagine a particle with position Pos and velocity Vel affected by acceleration Accel. Let’s say for the moment that the acceleration is constant. This is the case when only gravity is present.

A typical game engine loop will update position with regards to a timestep (often the duration of a frame) using the following method, known as Euler integration:

Particle::Update(float dt)
    Accel = vec3(0, 0, -9.81); /* Constant acceleration: gravity */
    Vel = Vel + Accel * dt;    /* New, timestep-corrected velocity */
    Pos = Pos + Vel * dt;      /* New, timestep-corrected position */

This comes directly from the definition of acceleration:

\[a(t) = \frac{\mathrm{d}}{\mathrm{d}t}v(t)\]
\[v(t) = \frac{\mathrm{d}}{\mathrm{d}t}p(t)\]

Putting these two differential equations into Euler integration gives us the above code.

Measuring accuracy

Typical particle trajectories would look a bit like this:

These are three runs of the above simulation with the same initial values.

  • once with maximum accuracy,
  • once at 60 frames per second,
  • once at 30 frames per second.

You can notice the slight inaccuracy in the trajectories.

You may think…

“Oh, it could be worse; it’s just the expected inaccuracy with different framerate values.”

Well, no.

Just… no.

If you are updating positions this way and you do not have a really good reason for doing so then either you or the person who taught you is a fucking idiot and should not have been allowed to write so-called physics code in the first place and I most certainly hope to humbly bestow enlightenment upon you in the form of a massive cluebat and don’t you dare stop reading this sentence before I’m finished.

Why this is wrong

When doing kinematics, computing position from acceleration is an integration process. First you integrate acceleration with respect to time to get velocity, then you integrate velocity to get position.

\[v(t) = \int_0^t a(t)\,\mathrm{d}t\]
\[p(t) = \int_0^t v(t)\,\mathrm{d}t\]

The integral of a function can be seen as the area below its curve. So, how do you properly get the integral of our velocity between t and t + dt, ie. the green area below?

It’s not by doing new_velocity * dt (left image).

It’s not by doing old_velocity * dt either (middle image).

It’s obviously by doing (old_velocity + new_velocity) * 0.5 * dt (right image).

And now for the correct code

This is what the update method should look like. It’s called Velocity Verlet integration (not strictly the same as Verlet integration, but with a similar error order) and it always gives the perfect, exact position of the particle in the case of constant acceleration, even with the nastiest framerate you can think of. Even at two frames per second.

Particle::Update(float dt)
    Accel = vec3(0, 0, -9.81);
    vec3 OldVel = Vel;
    Vel = Vel + Accel * dt;
    Pos = Pos + (OldVel + Vel) * 0.5 * dt;

And the resulting trajectories at different framerates:

Further readings

“Oh wow thank you. But what if acceleration is not constant, like in real life?”

Well I am glad you asked.

Euler integration and Verlet integration are part of a family of iterative methods known as the Runge-Kutta methods, respectively of first order and second order. There are many more for you to discover and study.

  • Richard Lord did this nice and instructive animated presentation about several integration methods.
  • Glenn Fiedler also explains in this article why idiots use Euler, and provides a nice introduction to RK4 together with source code.
  • Florian Boesch did a thorough coverage of various integration methods for the specific application of gravitation (it is one of the rare cases where Euler seems to actually perform better).

In practice, Verlet will still only give you an approximation of your particle’s position. But it will almost always be a much better approximation than Euler. If you need even more accuracy, look at the fourth-order Runge-Kutta (RK4) method. Your physics will suck a lot less, I guarantee it.


I would like to thank everyone cited in this article, explicitly or implicitly, as well as the commenters below who spotted mistakes and provided corrections or improvements.

  • Posted: 2011-12-14 00:39 (Updated: 2011-12-15 14:34)
  • Author: sam
  • Categories: rant code physics

Attachments (5)

Download all attachments as: .zip


1. mikarnage -- 2011-12-14 15:47


Nice explanation, I would have liked to see the case about what happens with a spring+mass+friction system : from experience, rather than just a slight loss in precision, you can get into cases where the system gets unstable and explodes, rather than just slowly decreasing in amplitude..

2. sam -- 2011-12-14 16:07

@mikarnage: I would like to write another article about RK4 to illustrate that! Verlet would still help in comparison with Euler, but higher-level methods are really needed. The bane of RK4 is that it is so simple, yet so hard to explain. I hope to be able to get to-the-point diagrams like this one:

3. geolm -- 2011-12-14 18:32

"Your physics will suck a lot less, I guarantee it" true but the CPU cost is too high... that's why havok still use that dirty-euler-integration. Anyway nice article :)


4. Richard -- 2011-12-14 21:55

Hi Sam

The term "Verlet integration" is more commonly used to describe Störmer's original method, which improves stability in some situations (e.g. with springs) by completely avoiding the use of the velocity when calculating the position. The method you have called "Verlet" goes by many names, including "Velocity Verlet" and "Improved Euler", but to simply call it "Verlet" is not strictly correct. It is, as you say, much better than the standard Euler integration.

This presentation I did some years ago may be of interest, towards te end it compares the Euler integration (explicit and implicit) with the improved Euler (aka velocity Verlet), the 4th order Runge-Kutta and the Verlet (Störmer's original) in various circumstances.

5. Richard -- 2011-12-14 22:09

Hmm, the link to the presentation didn't work. And I can't add it now because trac thinks I'm spamming. Sorry.

Also, geolm, I last used Havok many years ago and even back then they offered the choice of Euler integrator, velocity Verlet integrator, and 4th order Runge-Kutta. The default was Euler, but the others were offered. What made it particularly flexible is you could chose to use the more accurate integrators on specific objects only.

6. Promit -- 2011-12-14 22:24

Sorry, but using Verlet or RK4 is not a good idea in a physical simulation. Neither integrator is good at preserving energy properly in the system, so you can get pretty severe instabilities as things explode or grind to a halt. For game simulation purposes, you're vastly better off with the semi-implicit Euler method.

7. anonymous -- 2011-12-15 11:34


Why is this true? is it mistake?

I thought a(t) = dv/dt; v(t) = dp/dt;

8. Valentin Simonov -- 2011-12-15 11:34

Err, about your definition of acceleration. v(t) = d p(t) / dt a(t) = d v(t) / dt

I wonder how nobody else noticed this.

9. sam -- 2011-12-15 12:15

@Valentin: that is indeed a mistake! I'm gonna fix that immediately, thanks.

10. sam -- 2011-12-15 12:21

@Richard: thank you for the suggestions, I will make it clearer that it is not strictly Verlet. And sorry for Trac's aggressive antispam behaviour: it gets pounded extremely hard by spambots so the Bayesian filter has become trigger-happy. I will put the link back in your comment. (I use this blog system because it lets me write maths and format source code very easily, but it's clearly not the nicest engine out there).

11. marco -- 2011-12-15 12:33

Lol, love that article. Extremely well presented, keep up (good work, humour, ...)!

12. mmick66@gmail.com -- 2012-04-27 20:22

Is this method of averaging velocities not identical with RK2?

13. sam -- 2012-04-28 13:15

@mmick66: you are right, when acceleration is constant, Velocity Verlet and RK2 become identical.

14. TheodorC -- 2013-01-07 16:36

Hi Sam,

I did, not a long time ago, a small survey on popular explicit integration methods. What I found in terms of terminology (unintended wordplay) was that your "Velocity Verlet" is actually the same as the "midpoint method". You can find some of these popular integrators mentioned in Appendix A of this paper -> https://www.dropbox.com/s/nfj4it6jjugfhdp/DLOReport.pdf . As I understood it, Velocity Verlet requires using a velocity prediction to find the future position, then correct/update the velocity to obtain a somewhat more synchronized pair (pos, vel). Thus, Velocity Verlet would evaluate the acceleration twice per step: the first time to get the position, then to get the corrected velocity using the updated position and the velocity prediction. Is this view correct, or have I misunderstood it badly?

As a sidenote, it might be worth mentioning some of the traits of symplectic integrators (such as Verlet): they preserve energy for closed systems (or area if you consider a parallelogram of initial conditions). RK4 is not symplectic, although being more accurate than Euler, it still introduces energy in the system and can make it explode. I don't have the links now, but there were some articles mentioning the possibility of making RK4 numerically damp the solution, thus having a somewhat more increased stability (and, of course, no symplicity whatsoever).

All in all, great articles/posts on numerical issues and C++, the community is grateful for you sharing this knowledge in such a concise and pertinent way!

Best wishes, Theodor

15. mcintyre321@gmail.com -- 2013-04-10 17:51

What about storing the position and time the acceleration was last changed, and doing the calculation from there?

Also, should Vel = Vel + (OldAccel + NewAccel) * 0.5 * dt; and if not, why not?


16. martijnhh -- 2013-10-20 12:53

Hi Sam,

I wish i found out about this article earlier.. The visual you presented made things a lot more clear to me! I'm currently trying to get an idea of what the difference is between integrators, but got stuck pretty quickly before stumbling on your article. I get things better when they're presented in a visual way or analogy instead of dry formula's.

As much as your picture cleared up the difference between euler and verlet for constant acceleration for me, I was hoping you could maybe clear a couple other things im not sure about..

You visualize how the area of the verlet integration function is given by: (old_velocity + new_velocity) * 0.5 * dt. So this works better than euler in this specific case, because for a constant acceleration, the graph between the old & new pos would be connected by a line and thus it's area can be perfectly fitted by a trapezoid. Is it safe to conclude that just like euler already has errors for constant acceleration, verlet will have errors just like euler when integrating non constant acceleration? And the error for Euler will even increase in comparison to verlet?

I also read that energy can get lost or is kept equal with some integrators, what does this exactly mean? Has it to do with these errors that add up or decrement during integration?

Is the example that Richard gives in the gravity example (one of the last slides) an example of RK4 not losing energy?: http://www.richardlord.net/presentations/physics-for-flash-games The verlet integrator seems to realisticly come at rest while the rk4 keeps going.. or was it not supposed to come at rest and was this because of "energy leaking" from the system?

And is the gravity example given here an example of errors adding up for verlet in non constant acceleration?: http://codeflow.org/entries/2010/aug/28/integration-by-example-euler-vs-verlet-vs-runge-kutta/ And why would it perform worse than euler here?

Also this "stability" they sometimes talk about (mostly when discussing springs), how is that related?



17. Aktau -- 2014-03-01 20:44

Your posted method is a degenerate version of velocity verlet (which I'm sure goes by several different names, all of which are confusing), in the case of constant acceleration. The one for the case where you have an acceleration() function (usually the case I guess) is this: http://en.wikipedia.org/wiki/Verlet_integration#Velocity_Verlet

The difference with your method is the velocity, where you just do forward Euler on the velocity, normally velocity Verlet averages the current acceleration and the acceleration of the predicted position. You can keep this acceleration around for the next invocation so you save actually evaluate the force function only once. You'll make a small error in case the acceleration function depends on velocity (drag forces, ...) as well, but hey, can't win 'em all.

As wikipedia says, some implementations even add another correction step, not sure how much it helps but it looks cheap (just one FMA-op).

18. plasmacel -- 2015-09-23 16:30

Verlet methods are not part of the Runge-Kutta family of methods. The 2nd order Runge-Kutta method is Heun's method (so-called Improved Euler), which is similar to the Velocity Verlet, yet different. Verlet methods are symplectic (they conserve energy), which can't be said about the Runge-Kutta family.

27. online -- 2016-12-15 11:49

http://v9onlinepharm.com/ , For Men Price In Bangalore in League City .

56. XRumerTest -- 2017-05-09 19:57

Hello. And Bye.

158. anonymous -- 2017-06-18 20:39


159. Ders3vchMub -- 2017-07-15 03:02

local payday loans <a href=http://www.europromec.com/index.php?option=com_k2&view=itemlist&task=user&id=62913>payday loans reviews</a> payday loan companies not brokers <a href="http://impanagiotopoulos.gr/index.php?option=com_k2&view=itemlist&task=user&id=2751"> fair credit loans</a> indian reservation loans <a href=http://www.cathaybabycare.com.tw/index.php?option=com_k2&view=itemlist&task=user&id=415698>easyloan</a> quick loans for people with bad credit <a href="http://tennis.krata.ru/index.php?option=com_k2&view=itemlist&task=user&id=215860"> unsecured loans for you</a> usa cash <a href=http://sparta-fit.com/index.php?option=com_k2&view=itemlist&task=user&id=577912>24 month loans</a> cash loans <a href="http://sov2009.ru/index.php?option=com_k2&view=itemlist&task=user&id=178473"> online loan application</a> cash advance online <a href=http://littlebearonline.com/index.php?option=com_k2&view=itemlist&task=user&id=14855>money lenders online</a> small personal loans for people with bad credit <a href="http://www.haicscale.com/index.php?option=com_k2&view=itemlist&task=user&id=551066"> loans for emergencies</a> get a loan fast <a href=http://tennis.krata.ru/index.php?option=com_k2&view=itemlist&task=user&id=215498>need money today</a> easy quick loans <a href="http://focusteam.ma/index.php?option=com_k2&view=itemlist&task=user&id=430823"> online payday lenders</a>

160. Cdfg2fvhTup -- 2017-07-15 03:02

transfer money to bank account <a href=http://bcel.uk/index.php?option=com_k2&view=itemlist&task=user&id=1043392>short term loan</a> payday loans spokane wa <a href="http://mobility-corp.com/index.php?option=com_k2&view=itemlist&task=user&id=989660"> bad credit payday loans direct lenders only</a> online personal loan application <a href=http://www.mykoperasi.coop/index.php?option=com_k2&view=itemlist&task=user&id=2731187>monthly payday loans</a> bank personal loans <a href="http://www.yopougon.ci/index.php?option=com_k2&view=itemlist&task=user&id=522381"> loan bad credit</a> banks that offer personal loans <a href=http://www.lala-nathi.co.za/index.php?option=com_k2&view=itemlist&task=user&id=666491>same day loans</a> payday loans albuquerque <a href="http://boreyk.ru/index.php?option=com_k2&view=itemlist&task=user&id=87940"> how to get a loan with bad credit</a> direct line loans <a href=http://www.yopougon.ci/index.php?option=com_k2&view=itemlist&task=user&id=522381>loan guarantee</a> secure loan <a href="http://by.soudalvps.safistudio.pl/index.php?option=com_k2&view=itemlist&task=user&id=488382"> express loan</a> holiday money <a href=http://avtobox.com.ua/index.php?option=com_k2&view=itemlist&task=user&id=8252>payday loan online direct lender</a> get personal loan <a href="http://www.stefantheimer.de/index.php?option=com_k2&view=itemlist&task=user&id=193066"> personal loan no credit</a>

161. Ders3vchMub -- 2017-07-15 08:20

payday cash advance online <a href=http://lpm-display-konzepte.de/index.php?option=com_k2&view=itemlist&task=user&id=1077870>payday cash advance</a> lenders for bad credit <a href="http://radiosaba.com/index.php?option=com_k2&view=itemlist&task=user&id=20946"> load finder</a> emergency loans for bad credit <a href=http://www.yopougon.ci/index.php?option=com_k2&view=itemlist&task=user&id=522381>sameday loans</a> online payday loans <a href="http://misericordiaaguiardabeira.pt/index.php?option=com_k2&view=itemlist&task=user&id=19885"> online loan companies</a> online loans in texas <a href=http://yubecosmetics.com/index.php?option=com_k2&view=itemlist&task=user&id=134864>direct lenders for bad credit loans</a> personal loan company <a href="http://alinaqijahani.ir/index.php?option=com_k2&view=itemlist&task=user&id=515632"> online payday loans</a> personal loans comparison <a href=http://www.yopougon.ci/index.php?option=com_k2&view=itemlist&task=user&id=522381>loan in minutes</a> i need 1000 dollars now <a href="http://verticalview.it/index.php?option=com_k2&view=itemlist&task=user&id=737106"> payday loans no debit card</a> payday loan lenders bad credit <a href=http://www.stefantheimer.de/index.php?option=com_k2&view=itemlist&task=user&id=193066>apply for personal loan</a> loans without credit checks <a href="http://www.yopougon.ci/index.php?option=com_k2&view=itemlist&task=user&id=522381"> same day cash loans</a>

162. Cdfg2fvhTup -- 2017-07-15 08:22

payday loan for bad credit <a href=http://www.bedanto.ir/index.php?option=com_k2&view=itemlist&task=user&id=182441>actual payday lenders</a> no credit personal loans <a href="http://www.slinardos.gr/index.php?option=com_k2&view=itemlist&task=user&id=258921"> money lending sites</a> lenders network <a href=http://www.yopougon.ci/index.php?option=com_k2&view=itemlist&task=user&id=522814>borrowing money</a> loans for bad credit not payday loans <a href="http://www.greenacre.co.za/index.php?option=com_k2&view=itemlist&task=user&id=1806439"> check advance</a> personal bad credit loans <a href=http://www.greenacre.co.za/index.php?option=com_k2&view=itemlist&task=user&id=1807093>i need a loan with bad credit</a> high interest loans <a href="http://mobility-corp.com/index.php?option=com_k2&view=itemlist&task=user&id=990286"> non broker payday loans</a> direct payday lenders for bad credit <a href=http://yellowdevilz.com/index.php?option=com_k2&view=itemlist&task=user&id=485659>payday cash advance online</a> direct cash <a href="http://mobility-corp.com/index.php?option=com_k2&view=itemlist&task=user&id=989660"> how can i get money today</a> loan options <a href=http://hoasupportgroup.com/index.php?option=com_k2&view=itemlist&task=user&id=577448>online loans</a> payday loans las vegas nv <a href="http://spyroltd.com/index.php?option=com_k2&view=itemlist&task=user&id=997059"> online payday loans bc</a>

163. Cdfg2fvhTup -- 2017-07-15 16:21

i need a loan with bad credit <a href=http://speroda.org/index.php?option=com_k2&view=itemlist&task=user&id=6121>loansdirect</a> greenwood loans <a href="http://www.nds.com.pk/index.php?option=com_k2&view=itemlist&task=user&id=440436"> ez money loan</a> net pay advance <a href=http://www.selimiyecamii.nl/index.php?option=com_k2&view=itemlist&task=user&id=114168>loans in houston</a> direct cash lenders <a href="http://pasyvex.com/index.php?option=com_k2&view=itemlist&task=user&id=14865"> loans online bad credit</a> online lenders <a href=http://tennis.krata.ru/index.php?option=com_k2&view=itemlist&task=user&id=215860>bad credit personal loans for 5000</a> payday loans online direct lenders only <a href="http://www.nds.com.pk/index.php?option=com_k2&view=itemlist&task=user&id=440236"> payadvance</a> payday loans el paso tx <a href=http://autocaravanastenerife.es/index.php?option=com_k2&view=itemlist&task=user&id=93800>online personal loans</a> quick pay day loans <a href="http://afina-mos.ru/index.php?option=com_k2&view=itemlist&task=user&id=270356"> online cash</a> short term personal loans <a href=http://verticearq.com.mx/index.php?option=com_k2&view=itemlist&task=user&id=583022>how to apply for a personal loan</a> payday advance locations <a href="http://www.yopougon.ci/index.php?option=com_k2&view=itemlist&task=user&id=522381"> loan express</a>

164. Maria6ennvop -- 2017-07-15 23:15

online loans <a href=http://payday100loans3000online.com/>online loans</a> payday loan <a href="http://payday100loans3000online.com/"> loans online</a>

165. Dvur5fbhnip -- 2017-07-16 04:18

loan providers <a href=http://www.rcprofessionista.net/index.php?option=com_k2&view=itemlist&task=user&id=94839>personal loans for people with poor credit</a> online payday loans in texas <a href="http://pasyvex.com/index.php?option=com_k2&view=itemlist&task=user&id=14865"> fast cash now</a> advance loan <a href=http://sov2009.ru/index.php?option=com_k2&view=itemlist&task=user&id=178732>loan services</a> get a loan <a href="http://laprincesadeljamon.com/index.php?option=com_k2&view=itemlist&task=user&id=33205"> quick loans same day</a> bad credit loans online <a href=http://testserver7.amcomplete.com/index.php?option=com_k2&view=itemlist&task=user&id=132497>tax advance loans</a> quick personal loan <a href="http://argillic.com/index.php?option=com_k2&view=itemlist&task=user&id=961732"> online payday loans california</a> bad credit loans reviews <a href=http://psmbranding.com/index.php?option=com_k2&view=itemlist&task=user&id=653853>very bad credit loans</a> payday loan reviews <a href="http://hoasupportgroup.com/index.php?option=com_k2&view=itemlist&task=user&id=577822"> paydayloan com</a> emergency bad credit loans <a href=http://mobility-corp.com/index.php?option=com_k2&view=itemlist&task=user&id=990687>bad credit payday loan lenders</a> bad credit loans california <a href="http://ingespek.nl/index.php?option=com_k2&view=itemlist&task=user&id=20060"> direct payday loan lenders online</a>

167. Merlinbib -- 2017-08-19 10:18

<a href=http://www.acgproducciones.es/zapatos-hugo-boss-sport-625.html>Zapatos Hugo Boss Sport</a>

With so many contaminants within the oxygen, it may be challenging to identify by far the most probable cause for your sensitive symptoms. A lot of people just imagine that plant pollen is to pin the blame on. In fact, it could be everything from lawn fertilizer, to local animals, and natural plants and flowers. In such cases, you can easily come to be disheartened when 1 experiences a hypersensitive reaction even in the course of days and nights by using a very low pollen count up. An allergies analyze will help you to reach the base of your signs and symptoms.

<img>https://www.ttwater.it/images/creepers/3627-puma-creepers-mimetiche.jpg</img> Golf is performed all around the world and is probably the number of online games that lacks a standard area of engage in. Playing golf programs can differ broadly from location to location however most have possibly 9 or 18 pockets. Golf is a very social sports activity and is known as a discretion activity.Excellent Advice For Maximizing Your Weight Damage <img>https://www.gartex.it/images/gartex/12513-asics-gel-kayano-8.jpg</img>

169. Sarah Carlson -- 2017-08-20 13:46

This is a comment to the Blog: Understanding basic motion calculations in games: Euler vs. Verlet – Lol Engine webmaster. Your website is missing out on at least 300 visitors per day. Our traffic system will dramatically increase your traffic to your site: https://flxv.tk/6 - We offer 500 free targeted visitors during our free trial period and we offer up to 30,000 targeted visitors per month. Hope this helps :) Unsubscribe here: http://priscilarodrigues.com.br/url/11

170. James Kelly -- 2017-11-16 06:44

OH. MY. GOD. I was having the hardest time figuring out why my sprite was oscillating in my 2D project with it getting seemingly worse the more the sprite moved and I was ready to give up until I came across your article and my face when all the jitter was gone with just a single change in a line of code.

Thank you so much!

171. RD -- 2017-12-08 09:45

Neither of the two method you described are false or wrong. The first one is simply called semi-implicit Euler method. There are plenty of scenarios where semi-implicit Euler is fast and accurate enough and at the same time uses less calculations and memory. Particle systems as an example. If you have thousands of particle update per game loop cycle, have slightly less calculations might make a difference and at the same time, a perfect position of the particles is irrelevant and is hardly noticeable.

As you have mentioned, your method produces correct results only if acceleration is constant, which is hardly ever the case.

Maybe you should watch you language and be more careful about who you call a "fucking idiot" or others might judge upon you in the same way.

172. dissertation helpers -- 2018-01-11 07:32

Well thanks for posting such an outstanding idea. I like this blog & I like the topic and thinking of making it right. <a href="https://www.dissertationinc.com/">dissertation helpers</a>

173. Law Project Help -- 2018-01-11 11:31

We also share some information about our business https://lawassignmentshelp.com/

174. kaalus -- 2018-01-22 22:34

Accuracy is often less important than stability. The method you are proposing (midpoint) while more accurate, is less stable than plain Euler. You will be able to sustain stiffer forces without your system exploding by using plain Euler.

175. anonymous -- 2018-02-19 10:20

Thank you for your work on the blog! You're doing a good job! I would like to read about it anymore. Prompt, what literature to study?


176. anonymous -- 2018-07-16 18:19

Wegmans Food Markets is a privately held American supermarket chain. It employs thousands of people throughout their many store locations. Wegmans employees use an employee portal named https://mywegmansconnectt.xyz/www-mywegmansconnect-com/ Employee portal so that they can get every news from the company.

177. anonymous -- 2018-07-30 07:56

I really thank you for the valuable info on this great subject and look forward to more great posts. Thanks a lot for enjoying this beauty article with me. I am appreciating it very much! Looking forward to another great article. Good luck to the author! All the best! awakening movies https://mwge.org/

178. anonymous -- 2018-07-30 14:05

I found your this post while searching for information about blog-related research ... It's a good post .. keep posting and updating information. a course in miracles https://acim-online-video.net/

179. anonymous -- 2018-07-31 08:03

I would like to thank you for the efforts you have made in writing this article. I am hoping the same best work from you in the future as well.. <a href='https://acimcourses.com/'>acim</a>

180. anonymous -- 2018-07-31 22:54

Home Depot is the largest home improvement retailer in the United States. myTHDHR is the official online portal which is created to help the employees of Home Depot. https://surveyexperience.info/mythdhr/

181. anonymous -- 2018-08-02 07:35

Hello There. I found your blog using msn. This is an extremely well written article. I will be sure to bookmark it and return to read more of your useful information. Thanks for the post. I’ll certainly comeback. Mandani Bay http://mandanibay.residences.ph/

182. anonymous -- 2018-08-02 08:20

It is good to read such a valuable information and thanks for sharing it. Livewebtutors is striving towards creating a great learning platform and hence, provide authentic assignment help to make it more informative. Visit Us: https://www.livewebtutors.com/assignment-help

183. Ted Johnson -- 2018-08-04 08:48

The blog you have shared is very good. This is really interesting information for me. Thanks for sharing! I am offering dissertation help to students in UK at low price. visit Website: http://www.ukdissertationhelp.co.uk/

184. anonymous -- 2018-08-07 11:36

my assignment help review has helped many students to choose the right website. It has also helped the students to score good grades in their academics. Our writing services review will help you to find the best writing websites for your success. http://assignmentshelpreview.com/allassignmenthelp-com-reviews/

185. maxwillor@gmail.com -- 2018-08-08 09:59

This is an excellent post I seen thanks to share it. It is really what I wanted to see hope in future you will continue for sharing such a excellent post. Visit More: https://www.myassignmenthelpau.com/

186. anonymous -- 2018-08-13 08:25

I am happy to find this post very useful for me, as it contains lot of information. I always prefer to read the quality content and this thing I found in you post. Thanks for sharing. Visit here: http://www.myassignmenthelpsg.com/

187. nata -- 2018-08-21 06:43

If there are many sad stories, share it with the people you trust. Sharing helps people get closer together and you also relieve some of that sadness.


188. Olivia -- 2018-08-23 10:05

It's very interesting. I didn't know much about the motion in game, this post helps me much instagram search

189. anonymous -- 2018-09-08 18:47

You already found it, my friend. This post here will show you the easiest ways to Activate Capital One Credit Card and Activate Capital One Debit Card. The article here has been posted after proper researches and experiment on Capital One Card Activations. So, if you really want to activate Capital One credit card or Debit card quickly, you probably should refer this post and complete your card verification task.

<a href="https://cardsactivation.com/www-capitalone-com-activate-capital-one-activation/"> CAPITAL ONE CARD ACTIVATION </a>

<a href="https://cardsactivation.com/www-capitalone-com-activate-capital-one-activation/"> How You Can Activate Your Capital One Credit Card Online </a>

<a href="https://cardsactivation.com/www-capitalone-com-activate-capital-one-activation/"> capitalone.com/activate a-6 </a>

190. krogerfeedback -- 2018-09-09 07:55

Kroger Feedback: It is an American retailing company and United States’ largest supermarket chain and the second-largest general retailer and the twenty-third largest company in the United States.

It was founded in 1883 with just $400, and its headquarter

is on the Vine Street in downtown Cincinnati. It is supervised by Mr. W. Rodney McMullen

and his right-hand man Mr. Michael L. Ellis

<a href="http://kroger-feedback-survey.info/"rel="dofollow">Kroger Feedback Customer Satisfaction Survey - KrogerFeedback.com</a>

191. anonymous -- 2018-09-09 08:27

There are two ways by which cardholders can activate their credit cards.

Capital One Credit Card Activation Online Capital One Credit Card Activation Over Phone

How to activate Capital One Credit Card Online?

<a href="https://cardsactivation.com/www-capitalone-com-activate-capital-one-activation/"> activate.capitalone.com activate card </a>

<a href="https://cardsactivation.com/www-capitalone-com-activate-capital-one-activation/"> capital one customer service </a>

<a href="https://cardsactivation.com/www-capitalone-com-activate-capital-one-activation/"> capitalone.com/activate </a>

<a href="https://cardsactivation.com/chase-card-activation-www-chase-com-verifycard/"> chase credit card customer service</a>

<a href="https://cardsactivation.com/www-bankofamerica-com-activate-bank-of-america-activation/"> bank of america card activation</a>

<a href="https://cardsactivation.com/www-capitalone-com-activate-capital-one-activation/"> capitalone com activate platinum mastercard </a>

192. latest -- 2018-09-09 14:27

welcome back friends. today below on our website and in this article we are going to talk about the my as you all are waiting for the

<a href= https://comsurveys.com/">Panda Express Survey</a>

193. onlinesurveygroup7@gmail.com -- 2018-09-10 04:22

What a great information you shared with us, I am inspired by the method for the stage. It kept joined me regularly. Keep doing awesome. Thanks for sharing this blog article. <a href= https://onlinesurveygroup.net/">Polo Factory Customer Satisfaction Survey</a>

194. Assignment help online -- 2018-09-10 07:44

Psychology is the most crucial discipline which supports other disciplines as well. Students have to write essay assignments on the several topics of psychology which are assigned by teachers. Students Assignment Help provides the services of customer psychology assignment help to the students. https://www.allassignmenthelp.com/java-assignment-help.html https://www.allassignmenthelp.com/computer-programming-assignment-help.html

195. my surveys -- 2018-09-10 14:05

There is an online RaceTrac Survey performance managed on its official gateway at TellRaceTrac survey. Racetrac customers are required to join this Racetrac Survey and share their authentic and accurate feedback as per their own visit experience at their official website www.tellracetrac.com. By this survey, the company wants to know about the customer’s feedback, complaints, suggestions, reviews etc. RaceTrac Survey offering their customers to Win the Free Racetrac Coupon code for free food at Racetrac Retail Store.

<a href="https://my-surveys.com/tellracetrac-survey-www-tellracetrac-com/"rel=>www.tellracetrac.com application</a>

<a href="https://my-surveys.com/tellracetrac-survey-www-tellracetrac-com/"rel=>racetrack survey</a>

<a href="https://my-surveys.com/tellracetrac-survey-www-tellracetrac-com/"rel=>racetrac validation code</a>

196. my surveys -- 2018-09-10 14:07

The RaceTrac Customer Satisfaction Survey is a crucial ingredient to the company’s sustainability and growth. This is because satisfied and happy customers are easier to serve, up-sell, and retain. Therefore, it makes basic sense to carry out a customer satisfaction survey. If you recently bought gasoline or any other product at a RaceTrac station or convenience store, complete this simple online questionnaire and tell them what you thought about their products and customer service.

<a href="https://my-surveys.com/tellracetrac-survey-www-tellracetrac-com/"rel=>racetrack survey</a>

<a href="https://my-surveys.com/tellracetrac-survey-www-tellracetrac-com/"rel=>racetrac validation code</a>

197. kn -- 2018-09-10 16:59

Hi friends. today below on our website and in this article we are going to talk about the my as you all are waiting for the

<a href= https://onlinefeedbacks.info/burger-king-survey-mybkexperience-guest-satisfaction-survey/">Burger King Survey </a>

198. fg -- 2018-09-10 17:09

Hi Friends. today below on our website and in this article we are going to talk about the my as you all are waiting for the <a href= https://onlinefeedbacks.info/talktowendys-wendys-survey/"> TalktoWendys Customer Satisfaction Survet</a>

199. Make my assignment -- 2018-09-11 08:23

Get the make my assignment services by the expert writers at Students Assignment Help. Our experts are proficient in writing assignments without missing the deadlines as they have gained their degrees from the top universities around the world. For more info visit https://www.studentsassignmenthelp.com/make-my-assignment/

200. papasurvey -- 2018-09-12 07:16

Nice post! This is a very nice blog that I will definitively come back to more times this year! Thanks for informative post.


201. Assignment Help -- 2018-09-12 08:48

The above post has given reliable and genuine information about Assignment Help Australia. Looking forward to avail their eminent services. http://www.firstassignmenthelp.com/

202. marked85 -- 2018-09-13 10:39

Welcome to My official site:<a href=" https://mykfcexperience.center/"> MyKFCExperience </a>

203. wool -- 2018-09-14 06:53

please welcome to my site: <a href="http://Mycfavisits.com/"> MyCfa Visit Survey</a>

204. customer Survey -- 2018-09-15 05:53

welcome back friends. today below on our website and in this article we are going to talk about the my as you all are waiting for the


205. surveyforcustomers -- 2018-09-17 12:37

You ought to be a part of a contest for one of the finest sites on the internet. I will recommend this website! From https://surveyforcustomers.com/

206. No Bake Recepie -- 2018-09-17 12:39

https://surveyforcustomers.com/dgcustomerfirst/ from here you can win up to $1000 prize by taking Dollar General Survey.

207. AnnaClare -- 2018-09-17 17:27

Math for me is something very far and difficult for my understanding. So all my math works I ordered as others. Only writing some essays with the help of https://collegewritinglab.com/ I done by myself.

208. Susan -- 2018-09-17 18:22

As always, a very interesting article.Susan

209. smithliam984@gmail.com -- 2018-09-20 09:56

Thank you very much for providing the important information for me. I am working as an academic consultant in USA and offer Excellent Coursework Help Services to college students. http://www.mycoursehelp.com/

210. anonymous -- 2018-09-21 08:08

Credit or Debit card offers users numbers of benefits. Mainly card makes purchases and payments

a lot easier than you ever had imagined. Cashback, rewards, free gifts, credit points also are offered on using the cards.

<a href="https://activatecards.net/"> capitalone com activate platinum mastercard </a>

211. anonymous -- 2018-09-24 00:56
212. anonymous -- 2018-09-27 08:57

We are proud of our best assignments help Australia experts because of their dedication towards providing continuous support to students by helping them meet deadlines and scoring better grades. We understand how important academic assessments are in developing a student's career and future opportunities, this is why we take extreme measures to ensure that all our solutions are best-in-class. All students looking for Sydney assignment help can reach us and avail the best online assignment help Sydney from our academic experts. He starts disliking his school or college. But may come, he has to submit his assignment before the deadline, therefore he chooses to buy assignment online services available to him. To help students complete their assignments My Assignment Services is here to serve them with the best assignment help.

Visit us: -

https://www.myassignmentservices.com/ https://www.myassignmentservices.com/assignment-help-sydney.html https://www.myassignmentservices.com/buy-assignment-services.html

213. hinali -- 2018-09-27 12:17

How's your experience at Murphy USA Fueling Center? Tell to Murphy USA in the Customer Service Survey online at www.tellmurphyusa.com you have great chance to win this Murphy USA Sweepstakes. Murphy USA Customer Satisfaction Survey is available at its official website www.tellmurphyusa.com. <a href="https://newcustomersurvey.com/www-tellmurphyusa-com-murphy-usa-survey/"rel=>Murphy USA Survey</a>

214. ajivika99 -- 2018-09-29 08:58

click here:<a href=" https://pradhanmantriyojana.net/"> pradhanmantriyojana </a>

215. ajivika99 -- 2018-09-29 08:59
216. anonymous -- 2018-10-09 10:57

Hello My name is Sarah Smith and This is a very nice post. Thanks for sharing with us. Keep it up

Get the Best Of My Assignment Help in UK Visit- http://www.myassignmenthelps.org/

217. Eva Green -- 2018-10-10 12:19

https://www.smartsurveys4u.com/europcar-survey/ beautiful! This is really a great post. Thank you for providing this information. https://www.smartsurveys4u.com/boots-opticians-customer-feedback-survey/

218. Tina -- 2018-10-10 12:22

This is a very good tip particularly to those fresh to the blogosphere. Short but very accurate information… Thank you for sharing this one. A must read post! https://smartsurveys4u.com/

219. johnb6174@gmail.com -- 2018-10-11 12:23

I would like to thank you for the efforts you have made in writing this article. I am hoping the same best work from you in the future as well. Thanks... hualien attractions https://www.islandlifetaiwan.com/the-best-of-hualien/

220. malik.farhan72@yahoo.com -- 2018-10-11 19:22

Thank you very much for writing such an interesting article on this topic. This has really made me think and I hope to read more. hualien night market https://www.islandlifetaiwan.com/hualien-visitors-guide/

221. woom -- 2018-10-12 07:46

Nice blog, the article you have shared is good.This article is very useful. My friend suggest me to use this blog.

<a href="https://tellthebell.website/"> Tell the bell survey </a>

222. malik.farhan72@yahoo.com -- 2018-10-12 08:43

This is a good post. This post gives truly quality information. I’m definitely going to look into it. Really very useful tips are provided here. Thank you so much. Keep up the good works. LS1 Print https://www.ls1print.co.uk

223. David berry -- 2018-10-12 09:47

A very nice and informative post! Thanks for the information! best <a href="http://www.rushstatus.com/best-good-morning-images-quotes-wishes-sms-collection/">good morning images</a> for friends.

224. malik.farhan72@yahoo.com -- 2018-10-14 22:13

The website is looking bit flashy and it catches the visitors eyes. Design is pretty simple and a good user friendly interface. snowtimes.de https://www.snowtimes.de/

225. anonymous -- 2018-10-15 07:10

The information you have posted is very useful. The sites you have referred was good. Thanks for sharing... Passport Seva http://passportenquiry.in

226. anonymous -- 2018-10-15 09:43

Awesome and interesting article. Great things you've always shared with us. Thanks. Just continue composing this kind of post. Enjoy Mexico Villa Rentals https://enjoymexico.net/villa-rentals/

227. anonymous -- 2018-10-15 11:30

Good article, but it would be better if in future you can share more about this subject. Keep posting. pos4less https://pos4less.de/

228. anonymous -- 2018-10-16 08:01

Its a great pleasure reading your post.Its full of information I am looking for and I love to post a comment that "The content of your post is awesome" Great work. Enjoy Mexico Villa Rentals in Cabo San Lucas https://enjoymexico.net/villa-rentals-cabo-san-lucas/

229. anonymous -- 2018-10-17 07:44

It is imperative that we read blog post very carefully. I am already done it and find that this post is really amazing. Enjoy Mexico top desinations https://enjoymexico.net/top-mexico-destinations/

230. malik.farhan72@yahoo.com -- 2018-10-17 10:15

Your website is really cool and this is a great inspiring article. asbestos awareness training online https://www.natas.co.uk/online-asbestos-awareness-training-courses/

231. anonymous -- 2018-10-18 11:15

This is a great inspiring article.I am pretty much pleased with your good work.You put really very helpful information... megabucksranch.com http://www.megabucksranch.com

232. anonymous -- 2018-10-18 13:04

Awesome and interesting article. Great things you've always shared with us. Thanks. Just continue composing this kind of post. Taroko Gorge Tour https://www.islandlifetaiwan.com/tours/taroko-gorge-tour/

233. anonymous -- 2018-10-18 14:05

These are some great tools that i definitely use for SEO work. This is a great list to use in the future.. green island taiwan https://www.islandlifetaiwan.com/tours/green-island-taiwan-explorer/

235. anonymous -- 2018-10-20 12:24

Its a great pleasure reading your post.Its full of information I am looking for and I love to post a comment that "The content of your post is awesome" Great work. 10 evelyn http://10evelyn.nation2.com/

236. Mikeh213@gmail.com -- 2018-10-20 14:05

I just want to say I’m newbie to blogging and site-building and absolutely enjoyed your web-site. Any query about your product contact http://flipkartcustomercare.xyz/ here.

237. karwa chauth 2018 -- 2018-10-23 09:32
238. anonymous -- 2018-10-24 09:56

Great articles and great layout. Your blog post deserves all of the positive feedback it’s been getting. Vidare till bloggen nu http://blomquistundertak.se/tag/tips/

240. anonymous -- 2018-10-26 16:32

This blog website is pretty cool! How was it made ! Vidare till sajten nu http://malmofisk.se/tag/tips/

241. anonymous -- 2018-10-27 13:42

Sample Assignment provides the assignment help to the students of various universities at a low price. Our highly-experienced writers are available 24x7 for guiding the students for any academic help. Email us your details at info@sampleassignment.com


242. anonymous -- 2018-10-27 20:43

You have done a great job on this article. It’s very readable and highly intelligent. You have even managed to make it understandable and easy to read. You have some real writing talent. Thank you. Qixingtan Beach https://www.islandlifetaiwan.com/hualien-beach-guide/

243. altadefinizione -- 2018-10-28 15:46

Mineral models including a huge zeolite model and a model of the structure of diamond were used to great effect in the movie as Professor Sherman Klump, desperately trying to lose weight, takes a chemical cocktail that morphs him into the slimly obnoxious Buddy Love. The mineral models feature prominently as classic examples of Klump's laboratory equipment.


244. Michael jones -- 2018-10-31 07:59

Students could often find it tough to write their academic tasks. It could lead to they not getting desired grades in the academics. Opting for our assignment help online could be ideal for such students and they can get a complete assignment solution from us. https://www.allassignmenthelp.com

245. anonymous -- 2018-10-31 12:38

I am glad you take pride in what you write. This makes you stand way out from many other writers that push poorly written content. Ytterligare info om denna hemsida http://blogstance.eu/

247. anonymous -- 2018-11-01 12:28

hello, this is roxy smith. this is a nice post, thanks for sharing. Get the best perdisco assignment help in Australia. here: https://www.ozassignments.com/solution/perdisco-assignment-help

248. anonymous -- 2018-11-06 07:24

Well You really need to have look in this https://customersreview.org

249. anonymous -- 2018-11-07 12:13

Doston aapke subah subah uthne ke baad aap pehla kaam kya karte hain. Agar aap janna chahate hain ki kaise din ki shuruat karen to hum aapko aise collection dete hain jahan aap apne friends aur relative ko good morning images wish kar sake. <a href="https://www.freshbirthdaywishes.com/good-morning-images/">Good Morning images in hindi Quotes</a>

Aap raat me sote waqt jarur apne doston aur relatives ko yaad karte honge aur unhe bhi shubh ratri wish karte honge. hamare paas sundar images ke collection se aap unhe wish kar sakte hain.

<a href="https://www.freshbirthdaywishes.com/good-night-images/">Good Night images in hindi Quotes</a>

Naya saal bahut nazdik hai aur har koi uski taiyari karne me laga hai to aap kyun peechhe hain app bhi shuru ho jaiye aur wish kijiye unhe advance me happy new year <a href="https://www.freshbirthdaywishes.com/happy-new-year-sms-shayari-hindi/">Happy new year shayari sms hindi</a>

250. wtechniblog@gmail.com -- 2018-11-07 12:14

kya aap janna chahte hain ki google kya hai aur kaise bana to ye sirf aapke liye hai jankari. https://www.wtechni.com/google-kya-hai-hindi/

251. anonymous -- 2018-11-10 07:43

<b>This is a really good piece of information. I would love to visit your website again! Thanks</b> https://dailysurveyguides.com/panda-express-survey

252. anonymous -- 2018-11-10 07:44

I just started my day by reading your article! I really like the motivation! keep it up https://tellthebellsurveys.com/

253. anonymous -- 2018-11-10 10:55

The information you have posted is very useful. The sites you have referred was good. Thanks for sharing... CTFO Directory http://ctfodirectory.com/

254. anonymous -- 2018-11-11 02:21

Nice article really liked it Excellent Blog! I would like to thank for the efforts <a href="https://www.pcweek.in/2018/08/blogger-templates-without-copyright.html">blogger template without footer credit</a>

255. anonymous -- 2018-11-11 02:22

Excellent Blog! I would like to thank for the efforts https://fontawesomeicons.blogspot.com

256. anonymous -- 2018-11-11 06:24

Excellent Blog! I would like to thank for the efforts <a href="https://www.pcweek.in/2018/09/wilamp-universal-automation-app-arduino-esp8266.html">iot projects</a>

257. anonymous -- 2018-11-11 16:45

Excellent information on your blog, thank you for taking the time to share with us. Amazing insight you have on this, it's nice to find a website that details so much information about different artists. Air Duct Cleaning Shelby Twp MI https://www.sterlingheightsairductcleaning.com/

258. anonymous -- 2018-11-11 17:43

hey i loved your site layout and especially the way you wrote everything. I must say that you keep posting this type of information so that we may see the latest news. https://wijdanshahid.pk

259. aplha bravo -- 2018-11-12 05:53

hey i loved your site layout and especially the way you wrote everything. I must say that you keep posting this type of information so that we may see the latest news. <a href="https://surveyforcustomers.com">surveyforcustomers</a>

Add New Comment