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How to Calculate the Number of M&M's in a Container

Updated on December 11, 2016
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Have you have wondered how many standard sized M&M's would fit in a container? Perhaps you had the luxury of participating in a contest during your youth where the object was to guess the number of M&M's in a container. How did you fair? What approach did you take to figure it out? Well, there are many approaches to solving this problem. However, the most accurate method will likely involve the use of a formula derived from measurements of M&M's and their packing ratio (the percentage of space M&M's take up in a container).

During my research on the subject I found several derived formulae and many experiments completed by grade school students regarding the number of M&M's that will fit in a container. While many valiant efforts were made to solve this problem only a few people seemed to have computed valid results. One difficulty I encountered was simply finding published values on the mass, volume, and packing ratio of these multi-colored candies.

It also seemed that no scientists or organizations had taken credit for any specific formulas on the subject. Given the lack of sound information I decided to investigate this issue for myself. For me, the best approach was to use the average characteristics of an M&M to develop a simple formula to compute the number of M&M's in a container. I also wanted to compare these results to a simple quart container estimate that someone posted on a blog. And finally, I wanted compare both of these methods to an actual experiment.

Basic Characteristics of an M&M

American manufacturing processes are a marvel of modern engineering. Even so, there will always be some variability between every item that is produced on an assembly line. In the case of M&M's, the size, shape, and mass of each candy will likely vary to some degree. However, I'm sure that Mars, Incorporated has strict quality control standards and that the variability of these characteristics will likely be very small. With that said, I have scoured the internet to determine what the average value for an M&M's mass, volume, and packing ratio (this relates to the shape) are. The results are below:

Average characteristics of an M&M
Average characteristics of an M&M | Source

Formula For Computing Quantity of M&M's Based on a Container's Volume

I will use the average values shown above to derive a simple formula that can tell you the number of M&M's in a container based on its volume.

where the container's volume (V) is in fluid ounces.

where the container's volume (V) is in milliliters.

A Lone Blogger's Quart M&M Estimate

I once read a blog (now I can't find it to properly cite them) that said exactly 1,011 M&M's would fit into a 1 quart (946ml) container. I am not sure of the context of the measurement but it did seem to have been verified experimentally. Given this information, the Blogger's formula for computing the number of M&Ms in a container would have been:

where the container's volume (V) is in fluid ounces.

where the container's volume (V) is in milliliters.

Pink M&Ms
Pink M&Ms | Source

My Experiment

Formula's and calculations are great, but if they don't accurately predict something then they are useless. Therefore, I wanted to see how good these formulae were at predicting reality. I went to my local candy store and purchased a large bag of M&M's (my wife made me get pink). First, I selected several different sized containers and measured their volume by carefully seeing how much water they could hold. I filled the shot glass and the old pot to the very top for this experiment. I used the label's reported volume on the gallon jug and on the 9oz Dixie cup. Since I like the metric system better, all my measurements were done in milliliters.

Various containers and their respective volume used in this experiment.
Various containers and their respective volume used in this experiment. | Source

Next, I filled this containers with M&M's and proceeded to count how many each one held. As you can imagine this was a tedious process and there were many M&M casualties.

Results and Comparison to the Calculations

So how did these formula's do when comparing to a real life experiment? Pretty good actually. The table below shows the number of M&M's that can fit in to a variety of container sizes compared to the numbers predict by the formulae shown above.

Container
Container Volume (ml)
My Experiment
Blogger Formula
My Formula
Shot Glass
39
41
41.7
42.0
9oz Dixie Cup
266
280
284.3
286.5
Large Measuring Cup
1000
1055
1068.7
1077.0
Old Pot
2100
2211
2244.3
2261.8
1 Gallon Jug
3785
3995
4045.1
4076.6
Measured and computed number of M&Ms for various containers.

The graph below shows a visual representation of the information found in the above table.

I recently purchased this King Gumball Machine for my kids. It holds about 5lbs of M&Ms (about 2,350 of them).
I recently purchased this King Gumball Machine for my kids. It holds about 5lbs of M&Ms (about 2,350 of them). | Source

From this information we can draw some very interesting conclusions:

  • The blogger's formula was more accurate than my formula at predicting the number of M&M's
  • The blogger's formula is at most 98.8% accurate for containers of 1 gallon or smaller
  • My formula is at most 98% accurate for containers of 1 gallon or smaller
  • Both formulae computed values within 0.8% of each other for containers of 1 gallon or smaller
  • The larger that the container is, the less accurately the formulae is able to predict the true number of M&M's in the container.
  • The container's shape effects the number of M&M's that it can hold
  • Counting M&M's takes a long time

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    • calculus-geometry profile image

      TR Smith 3 years ago from Germany

      Cool experiment. From your table it looks like you'll get a good estimate if you use the rule of 1051 - 1055 M&Ms per 1000 mL of volume. By the way, how did you determine the packing ratio of 0.685? Just by experiement, or something mathematical?

    • CWanamaker profile image
      Author

      CWanamaker 3 years ago from Arizona

      Hello Calculus-Geometry.

      I found a paper on the University of Delaware's Department of Mathematical Sciences website that stated that the packing ratio of an M&M (spheroid) is 0.685. This was based on the results of a group of students' experiments.

      This does differ from the packing ratios that I calculated from my own experiment which hovered around 0.67. I didn't want to use my own value to derive the formula because I wanted something to compare the results of my experiment to. I also felt that the 0.685 value was more reasonable based on my research. I suspect the difference in results has to do with the type of containers I used as well as the fact the volume of an M&M varies from sample to sample.

      As always, thanks for reading!

    • Frienderal profile image

      Frienderal 2 years ago from Singapore

      Interesting hub! With this formula at hand, I can finally confront interviewers who ask questions like how many M&M's into this container, etc. Thanks!

    • Arco Hess Designs profile image

      Arco Hess 2 years ago from Kansas City, Kansas

      Very interesting. I've seen these contests around town and have often wondered how anyone could possibly get close to the correct answer. Now I know. Math!

    • Sharkye11 profile image

      Jayme Kinsey 2 years ago from Oklahoma

      Interesting! I thought it was just a matter of taking a wild guess! Or filling up a similar sized container then counting the M&M's. I've never tried guessing the candy, but I won a lunch once for estimating how many dollars worth of dimes were in a jar. I have more experience with money than candy! Fascinating hub, will share!

    • Patsybell profile image

      Patsy Bell Hobson 2 years ago from zone 6a, SEMO

      How fun. M&M math. Nice to meet the M&M researcher.

      Voted up, Pinned

    • mySuccess8 profile image

      mySuccess8 2 years ago

      Interesting simplified formula you have derived for this computation, with a sufficiently good accuracy for this purpose. As you have rightly done, one of the critical factors that determine the formula accuracy is the “container shapes and sizes”, that can greatly affect how well or the number of the items (M&M’s) that can be packed into these various-shaped containers. Congrats on Hub of the Day!

      (Note: There seems to be one typo error for the second formula under the section “A Lone Blogger's Quart M&M Estimate”, where the statement “where the container's volume (V) is in fluid ounces” should be “where the container's volume (V) is in milliliters.”)

    • PaigSr profile image

      PaigSr 2 years ago from State of Confussion

      Not something that I had thought about before. Usually it was a best guess. And as a side note - bring back the light brown M & M's.

    • oceansnsunsets profile image

      Paula 2 years ago from The Midwest, USA

      What a fun and interesting hub! Thanks for sharing what you found with your own investigation into the subject. There can be times where this could be handy to know. I have seen it done with jellybeans, and the like. It's a fun thing! Good work!

    • heidithorne profile image

      Heidi Thorne 2 years ago from Chicago Area

      Finally, some math we can all appreciate! (Actually, I love these kinds of brain busters.) Very deserving Hub of the Day! Voted up, awesome and sharing with my followers on Twitter & LinkedIn next week!

    • DzyMsLizzy profile image

      Liz Elias 2 years ago from Oakley, CA

      Congrats on HOTD! Very funny and interesting topic, and so voted.

      I've never done well at these kinds of guessing games, and I suck at math, so I'll just take your word for it! LOL

    • Millionaire Tips profile image

      Shasta Matova 2 years ago from USA

      I'm sorry, I couldn't read any more after I found out that M&Ms had been hurt in your experiments. Congrats on your HOTD, casualties and all. LOL

      This is interesting. They have this contest at work for fund raising purposes, and I usually just make up a number. I'm going to have to take a more scientific approach from now on.

    • Adam Lee Andersen profile image

      Adam 2 years ago from Overland Park, Kansas

      Lol, awesome. Now I can impress my buddies every time I walk by an M&M dispenser. One question what about M&M'S with Almonds? Oops

    • baranitharan 2 years ago

      I've never done well at these kinds of guessing games, and I suck at math, so I'll just take your word for it! LOL

    • eugbug profile image

      Eugene Brennan 2 years ago from Ireland

      "M&M casualties" ? Does that mean you murdered them by eating them!

      Sands settles and packs better when shaken, does this apply to M&Ms?

    • CWanamaker profile image
      Author

      CWanamaker 2 years ago from Arizona

      Eugbug - Yes I chowed down on those M&Ms! I'm sure. A little bit of gentle shaking would probably help pack them down a little more I'm sure.

    • Romanian profile image

      Nicu 2 years ago from Oradea, Romania

      I like a lot M&M, and I was curious to know these details.

    • Anne Harrison profile image

      Anne Harrison 2 years ago from Australia

      Love the article - I hope no M&Ms were harmed in the experiment!

    • PDXBuys profile image

      PDXBuys 23 months ago from Oregon

      I could not have done this because my M&M snacking during the experiment would have skewed the results.

    • CWanamaker profile image
      Author

      CWanamaker 23 months ago from Arizona

      PDXBuys - I was fortunate enough to have enough extra M&ms to complete the experiment while still eating them haha!

    • Blond Logic profile image

      Mary Wickison 22 months ago from Brazil

      This is very interesting. I have seen these questions before, and never knew where to start to calculate it.

      Voted up, and shared.

    • rebeccamealey profile image

      Rebecca Mealey 22 months ago from Northeastern Georgia, USA

      "Quesstimation" is an important skill. Love this!

    • CWanamaker profile image
      Author

      CWanamaker 22 months ago from Arizona

      I was at a party recently where the host had a jar of M&M's and asked everyone to guess. I came within 10 M&M's but unfortunately did not win. Some lucky gal guessed the exact number!

    • the rawspirit profile image

      Robert Morgan 17 months ago from Hutchinson Island, FL - Myrtle Beach, SC - Scottsdale AZ

      I just wish you had been my math teacher. I would have excelled. Thanks for a great hub. Bobby

    • Eric 8 months ago

      Thanks. Googled this at the baby shower. Used your values and won. I would upload a pic if you had an option.

      Basically I compared your preset values to the most close shape which was a measuring cup.

      YAy. I won.

      Cool deal

      Eric

    • CWanamaker profile image
      Author

      CWanamaker 8 months ago from Arizona

      Eric,

      Congratulations, that's pretty awesome! Glad I could help.

    • Patrick 6 months ago

      Am I wrong, or do the "blogger" formulas make no sense?

    • Patrick 6 months ago

      Nevermind, I see it now.

    • Brendan Harris 6 weeks ago

      It's very possible I'm missing something, but the conclusions of this experiment as written above have some mistakes.

      The second conclusion should read "at most", not least, for 1 gallon or smaller, and 98.7 if we're rounding to the tenths. You might include that it's at least 98.3% accurate, too.

      The third conclusion should read "at most", not least, just as for the second conclusion. You might also include that it's at least 97.6% accurate.

      The fifth conclusion is incorrect, as both tend (though not perfectly) to become more accurate the larger the container.

      I'll take your word on the last conclusion! Actually, I intend to fill an object that I hypothesize will have the greatest experimentally verified packing factor, greater even than the 0.671 that you obtained with the largest container.

      I was drawn to this article as I've always been drawn to numbers, tables, formulas for predicting values and such. I truly appreciate the hard work put into doing this. For the purposes of reproducibility, might you share what technique you used for arranging the M&M's in the containers? By this I mean did you merely drop them in, or was there a settling process used.

    • CWanamaker profile image
      Author

      CWanamaker 6 weeks ago from Arizona

      Hello Brenden,

      I agree with your first and second points - a slight error in wording on my part. However I disagree on your third point because as the container gets larger (and thus the volume gets larger) the equations predict values that are further and further away from the true value (the number of M&M's I counted). I've illustrated this by adding a graph to the article which you can visually see that the distance between the predicted and true value increases as volume increases.

      To answer your last question I simply poured the M&M's into the container to fill it. I did not shake them to make them settle nor did I take any time to place them by hand. Had I done that I would have surely been able to fit more M&M's into the containers.

      Thanks for reading,

      Cwanamaker

    • NSJ135 4 weeks ago

      Thank you for posting this article. I literally just won a 43" TV at a work Christmas party because of your math. Cheers!

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