How many M&M’s are in the jar?

Last Thursday, there was a company-wide party. That morning, they put a big jar full of M&M’s (regular, not peanuts) at the lobby of the Truchard Design Center. You were supposed to estimate how many M&M’s were in there. Whoever makes the best guess, wins a $50 Gift Certificate at Best Buy (and everlasting glory).Continue reading for details on the complicated process involved in this chocolatey adventure.Step 1: What is the size of an M&M?

Find a caliber (Gustavo Castro let me use his digital caliber) and measure a bunch of chocolates. Average the sizes, calculate the volume of a single M&M. In case you’re curious: .636 cubic centimeters.

The measurements could not be repeated for verification… sample chocolates were eaten.

Step 2: What is the size of the jar?

There were no special rules about not getting near the jar. Take some measuring tape and get the perimeter of the jar, then the height of the volume occupied by M&M’s (not counting air between them – yet). Measure the thickness of the glass. Don’t forget concave base and the round corners of the jar. Then calculate the volume.

This is the jar full of m&m’s

Step 3: How much volume do the M&M’s really occupy?

Because of their unique shape, M&M’s occupy a percentage of the volume of the container when poured randomly. I didn’t calculate this… physicist Paul Chaikin and chemist Salvatore Torquato did all the hard work. I remember reading about it months ago, and Google helped me find their study. So, m&m’s poured randomly occupy 68% of the volume calculated above.

Paul Chaikin (left), professor of physics, and Salvatore Torquato, professor of chemistry, used M&M’s candies to reveal fundamental principles governing the random packing of particles at Princeton University. Photo: Denise Applewhite (2004).

With all these numbers, I came up with my answer…. 8608.9669. So I wrote 8608 and submitted my answer.

To the astonishment of everyone who saw me measuring chocolates that morning, I was almost dead on.

So how many M&M’s were really there?

The number of M&M’s in the jar was: 8609. I missed by one. I stupidly rounded down… unbelievable. Fortunately I still won the contest.

And for those who care… this is the breakdown by color (aproximate):

  • 1119: Brown
  • 1205: Yellow
  • 1119: Red
  • 2066: Blue
  • 1722: Orange
  • 1371: Green

[Update October 30th, 2007] Seriously people, I posted detailed instructions on how to calculate this thing. I’m not going to go solve your version of the problem if you request in the comments, no matter how nicely you ask. Now, if you send me a nice PayPal donation for the maintenance of this site, I just might :).

77 thoughts on “How many M&M’s are in the jar?”

  1. I am trying to figure out how many m& m’s are in a 1 gallon jar approximately 12 inches high and 22 inches in perameter.

  2. if the jar is 1 gallon, and it’s full to the top, then you have all you need:

    1 US gallon = 3 785.4118 cubic centimeters
    1 m&m = .636 cubic centimeters
    m&m’s pack 68% of the volume.

    That’s all you need to know!.

    If the jar is not 100% full, estimate how full it is and use that volume.


  3. Assuming 12 inches high and 22 inches in circumference is measured in from the INSIDE of the container your answer is:

    Constants/Assumtions and Formulas:

    2.54 cm = 1 inch
    0.636 cm^3 = volume of 1 M&M
    68% = packing density of plain chocolate M&M’s
    2 * pi * r = Circumference Of Circular Jar
    h * pi * r^2 = Volume of Cylindrical Jar

    1. Convert Inches to cm:

    12 inches = 12 * 2.54 = 30.48 cm
    22 inches = 22 * 2.54 = 55.88 cm

    2. Calculate the radius using the Circumference:

    r = 55.88 / (2 * pi)

    3. Calculare the volume using the radius and height:

    V = 30.48 * ((55.88 / (2 * pi)) ^ 2) * pi

    4. Divide volume by the volume of 1 M&M

    # of M&M’s = (30.48 * ((55.88 / (2 * pi)) ^ 2) * pi) / 0.636

    5. Adjust for the packing density of 68%

    # of M&M’s = ((30.48 * ((55.88 / (2 * pi)) ^ 2) * pi) / 0.636) * 0.68 = 8097.8493 M&M’s

    6. Round to whole M&M’s


    Note: Your container’s dimensions calculate out to 2 gallons and not 1.
    1 gallon = 231 inch^3 and
    12 inches * ((22 inches / (2 * pi)) ^ 2) * pi = 462 inch^3 so 462/231 = 2 gallons

  4. This is a great formula, someone should turn it into a calulator with selections for different size containers (gallons, quarts, liters, etc.) Great site, thanks!

  5. It’s left as an exercise to the reader to calculate.
    You can figure it out by filling up a bucket of a known volume with peanut M&M’s, and then counting them.
    Then calculate the volume of a single peanut M&M. Since the size is irregular, measurements may not work as well as they did on regular M&Ms.
    You could take a measuring cup and fill it up to a certain level with water. Drop 10-20 peanut M&M’s and see how much the water level rose (measure quickly before the M&M’s start soaking up too much water or disolving).

    If you do the measurements, please post your results here.


  6. I’m stymied. How do I calculate the volume of an (somwhat) irregular shaped jar (assuming I can’t empty it and fill it with water). My jar is mostly cubic 9cm per side(if it were straight) and filled with 9cm of m&m’s. Problem is jar is slightly rounded at the four corners. Is there some way to account for this or should I just guess like any normal person would?

  7. I am puzzled with the same problem. I am trying to determine the number of small chocolate eggs are in a vase that is 8″ across, and 24″ high. What do you suggest?

  8. My suggestion is to find out the packing ratio of the chocolate eggs experimentally. You do this by filling a container of known volume with these eggs and then counting the eggs. Read the procedure in the original post above and it should give you a very good idea of what needs to be done.

  9. Does anyone know how big one of those clear glass pumpkin candy jars is? I know that question may be obscure, but I can’t really obtain any more info. Thanks.

  10. Help! I have a jar that contains a combination of plain m&m’s and skittles. The jar is 7 1/8″ tall, 1/16″ thick, 4 1/2″ wide and the candy measures 6 1/4″. Can someone tell me how many pieces of candy are in this jar?

  11. I need your help!!!!… im trying to figure out how many m & m’s CHOCOLATe m & ms will fit in 1 x 20 container…. measurements are 5.900mLength x 2.352Width x 2.393M height…. could really do with a answer as soon as possible my friend pls!!!

  12. P&O / Maersk people are here trying to win an 20GB I-POD. Hahaha…

    anyway, i have my own answer in mind :p

    All the best!

  13. It is a trick question, the answer is really none because it is bad practice to put a container on its end. Anybody who knows anything knows that. 😉

  14. I find it very pathetic that Maersk employees need someone to tell them the answer when everything was explained in full detail above. It´s a first degree equation for crying out loud! You don´t deserve to win this thing if you´re that dumb.

  15. I’m doing a math project on this exact stuff, and I was wondering if there is a formula for how much volume an object would occupy! Thanks for helping!

  16. I was hoping there was a formula for calculating how much space an object occupies. (ex: M&M’s are 68%)

  17. OK, this is the information I was searching for, however, I found another website with conflicting information.
    This website claims that M&M’s are 0.45239 cc instead of .636, and pack at 59.69% instead of 68% as this website says.
    Also, what is wrong with rounding down? Because even if, for example, 589.9 fit, you can’t fit .9, so only 588 will fit the way I see it.

  18. Do you have the volume of a single PEANUT m&m? Thanks so much for point this into simple terms!!

  19. also, if you haven’t noticed by the picture, there are m&ms w/ peanuts mixed with plain ones in the jar.

  20. Cheating kinda takes the fun out of the tPF thing, doesn’t it? Anyway, there are over 100 pages of guesses, someone is bound to have guessed it by now. Cheaters never prosper! 😛

  21. HELP!!! i want to know how many m&ms are in a 2000 mL container, however i did the calculations and there doesnt seem to be that many in the container… i dont know what i am doing wrong… please help!!!

  22. Here is what I have……

    Regular M&Ms, in a 64oz container

    My guess is 64oz=1,892,706 ml x .636(each M&M) / 70%(volume of the jar used) = 1,719.6585 or 1,720 M&Ms

    What do you think???

  23. Hi, I’m trying to figure out how many m&m’s (plain, not peanut) are in a 5 gallon (abita water) jug. The winner receives a $200 to best buy. If there’s any way you can help, please let me know.

  24. I can help.

    The calculation method is spelled out IN GREAT DETAIL above, with dozens of examples. It’s bad enough that we’ve let someone else do all the hard work and figure out the calculations for us, but do you need an answer given to you? Look at the post just before yours, for crying out loud.

    64 oz = 1/2 gallon. How many half gallons in 5 gallons? Yowza! All you have to do is take the last guy’s answer and multiply it by ten.

    . . .

    I bet you had to use a calculator for that, didn’t you?

  25. My employer had one of these contests and I found the volume of a peanut was around .111 cubic inches. They haven’t announced the winner yet but they told me I was within 20. I used a machinists rule and the ellipsoid formula for volume, it’s just a variation of the sphere volume formula. lwh=length width and height, r = radius. 4/3*pi*Lr*Hr*Wr. I used 6 peanut mms and took the average. I’m trying to get a hold of a micrometer to get better measurements. I know it’s not the most exact form to find volume but I dont grad cylinders or flask to calculate displacement. Lemme know if anyone get a similar number. Oh, and .111 cubic in. is about 1.823 cc

  26. How do you fint the Volume for an M&M?
    like the simplest way you could put it into a formula ? ? ?

  27. how do you find the volume of an M&m (formula)?


    whats the percentage formula?

    ASAP please thanks

  28. well i need help

    there is a 5 gallon (abita)water jug containing m&m”s in it how many m&m’s can fit in the jar?? i kno the method just want to check my answer!!! but im thinking about (17,200) please get my answer A.S.A.P. thx a million…

  29. ……. continuing from the last post … the amount of m&m’s represent a number of drug related deaths last year that is as specific as i can get because thats all that they provided to me!! but i dot kno what drug what state or anything that is all that i kno!! so get my answer soon please!! (PS)thx

  30. You rock. i love this nd now i am gunna go out and win with all the other sucker 10 yr olds.

  31. fu you were wrong the jar looked exactly like the jar above and there were only 505 green. you loser fu all for making me lose. FFFFFFFFFUUUUUUUUUUU!!!!!!!!!!!!!!!

  32. damn you all!!! you are all nerdy losers that made me lose. so until later FFFFFFFFFUUUUUUUUUUU!!!!!!!!!!!!!!!!!!!!

  33. I found someplace that said the volume of a plain M&M was 1/3 the volume of a peanut M&M. I won’t know if I won until next week!! They tried to trick me up by putting half peanut M&Ms and half plain M&Ms but I figured a way around that by halving the height and creating two formulas.

  34. Hey Mystic,
    I don’t think what you’re saying works: It’s not about the volume, but about the packing density, which is determined by the shape of the M&M’s. The packing density of mixed peanut and plain M&Ms is not going to be just an average of the corresponding volume.

    Good luck though!

  35. First off, I stumbled across this site purely as part of my Internet travels (I’m not trying to win any contests or anything), and I think the work this guy has done is absolutely fantastic! He did his due diligence, solved a real-world problem, and was gracious enough to post his findings for the betterment of society.

    …Which brings me to my second point. To the people who are asking for help: you’re all idiots. The solution is clearly explained; all you need to do is actually read it and follow the steps. He even did the measuring of the M&Ms for you, and reported his findings. Your laziness, ineptitude, inability to think for yourselves, and need for instant gratification are causing the decline of this country’s global scientific and mathematic standing, but I digress. To the people who are actually posting replies to these ninnies: STOP THAT. I understand your desire to be helpful (and show off at the same time), but you’re just enabling these nitwits to coast along, reaping the benefits of your labor, and further accelerating America’s downward spiral into the depths of ignorance, stupidity, and complacency.

    *sigh* Slightly off-topic, I know. But what happened to American hard work and ingenuity, and having the best and brightest minds in the world? What happened to the Manhattan Project, inventing the Internet, and sending men to the moon? Seriously, people. If you can’t even calculate [from formulae that are handed to you, gratis, no less] how many M&Ms are in a jar, you don’t deserve any of these things.

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