How to Calculate the Number of M&M's in a Container
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 ratios of these multicolored 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 of my doing.
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:
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.
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 very 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.
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 predicted 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

The graph below shows a visual representation of the information found in the above table.
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
 M&M's are delicious
Questions & Answers
© 2013 Christopher Wanamaker
Comments
What type of M&M did the formula work with?
how many M&MS would fit in a jar 9 1/2 CM top, 10 1/3rd length and 11CM Bottom
In the first part of the equation where did you get 0.0215?
Very interesting and I often wondered how many M&Ms were in a few containers where I saw contests. The times I guessed, I wasn't even close. M&Ms are one of my favorite candies When I go shopping at BJs I buy the 56 ounce bag and tell my wife they are my medicine. It must be right they do make me feel better.
I have a cylindrical vase 11.75" high and 4.4" in radius. How many M&m would fit in this vase ?
FYI  There was a 2,000 ml mason jar at my daughter's dance studio that was filled just above the 2,000ml mark. Based on this post, we guessed 2,118. We lost. There were 1,971.
Thank you for a great article. I am scheduled to give a talk about work and play to my son's middle school class and this is very helpful information.
On another M&M related topic, color distribution, here is another interesting article from a scientist at SAS.
How many m&m are in a 2lb 10.0 oz bag?
Thank you for posting this article. I literally just won a 43" TV at a work Christmas party because of your math. Cheers!
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.
Nevermind, I see it now.
Am I wrong, or do the "blogger" formulas make no sense?
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
I just wish you had been my math teacher. I would have excelled. Thanks for a great hub. Bobby
"Quesstimation" is an important skill. Love this!
This is very interesting. I have seen these questions before, and never knew where to start to calculate it.
Voted up, and shared.
I could not have done this because my M&M snacking during the experiment would have skewed the results.
Love the article  I hope no M&Ms were harmed in the experiment!
I like a lot M&M, and I was curious to know these details.
"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?
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
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
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.
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
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!
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!
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.
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 variousshaped 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.”)
How fun. M&M math. Nice to meet the M&M researcher.
Voted up, Pinned
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!
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!
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!
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?
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