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

Chris has a Master's degree in engineering and uses his knowledge to write about a variety of topics from an analytical perspective.

A delicious pile of M&M's.

A delicious pile of M&M's.

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 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 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:

Average characteristics of an M&M

Average characteristics of an M&M

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.

how-to-calculate-the-number-of-mms-in-a-container

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

how-to-calculate-the-number-of-mms-in-a-container

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:

how-to-calculate-the-number-of-mms-in-a-container

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

how-to-calculate-the-number-of-mms-in-a-container

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

Pink M&Ms

Pink M&Ms

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.

Various containers and their respective volume used in this experiment.

Various containers and their respective volume used in this experiment.

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.

ContainerContainer Volume (ml)My ExperimentBlogger FormulaMy 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.

how-to-calculate-the-number-of-mms-in-a-container
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).

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

Question: How many M&M's are in a Mason Jar?

Answer: There are several types of mason jars. However, the most common ones are quart and pint-sized. Based on the formula in the article, the amount of M&M's a mason jar can hold is as follows:

A quart sized mason jar is 32oz in size and would be expected to hold about 1,019 M&Ms.

A pint-sized mason jar is 16oz in size and would be expected to hold about 509 M&Ms.

Question: How many M&Ms are there in 1 cup?

Answer: A standard cup has a volume of eight ounces. If you use the formula mentioned in the article, a cup should be able to hold approximately 255 M&Ms depending on the cup's shape.

Question: How many M&M's are there in large, 62oz pantry sized jar?

Answer: Based on the formula in the article, a large 62 oz pantry sized jar should be able to hold about 1,975 M&Ms. However, since this is a large container, the formulas in the article tend to overestimate the number of M&Ms by about 1% or so. Therefore, if I had to guess the number of M&M's in a container of this size, I would recommend rounding down to about 1,950 M&M's.

Question: How many M&Ms are in 3/4 cup?

Answer: Since 1 cup is 8 ounces, 3/4 cup is equivalent to 6 ounces. Based on the formula in the article, a 6oz container (3/4 cup) should be able to hold about 191 M&Ms.

Question: How many M&M’s are in a baby bottle?

Answer: Baby bottles come in various shapes and sizes which makes answering this question difficult. I am assuming that based on your question you may be referring to a baby shower game where everyone has to guess the number of M&M's contained in a baby bottle. In this case, they are most likely using a standard 8oz baby bottle. For an 8oz baby bottle, we would expect to find that about 255 M&M's can fit into it. If they are using a smaller 4oz baby bottle, I would wager that it could hold about 127 M&M's.

Question: How many M&M’s can fit in a school bus?

Answer: Based on my research, a typical school bus might have internal dimensions of 24ft X8ft X6ft. If we assume that 95% of this space is available to be occupied by M&M's, the volume becomes:

24x8x6x0.95 = 1094.4 cubic feet. There are 7.48052 gallons in each cubic foot and 128oz in each gallon.

Therefore, the total available volume in ounces is:

1094.4x7.48052x128 = 1,047,895.2ounces

Using the formula in the article we get:

1,047,895.2x0.685/0.0215 = 33,386,427.8 M&Ms.

Since we made a lot of assumptions I would say that about 33 million M&M's will fit inside of a school bus.

Question: How many M&M's can fit inside of a 3.4oz mason jar?

Answer: This is a small mason jar. Note that 3.4oz is roughly 100ml. Using the formula in the article, I calculate that about 108 M&M's should fit inside of this mason jar.

Question: How many M&Ms are in a 72 ounce jar?

Answer: Based on the formula in the article, a 72 oz container should be able to hold about 2,275 M&Ms. However, since this is a large container, the formulas in the article tend to overestimate the number of M&Ms by about 1% or so.

Question: How many M&Ms are in a 62 ounce container?

Answer: Based on the formula in the article, a 62 oz container should be able to hold about 1,975 M&Ms. However, since this is a large container, the formulas in the article tend to overestimate the number of M&Ms by about 1-2% or so.

Question: How many M&M's fit in a 25 oz water bottle?

Answer: Based on the formula in the article, a 25oz water bottle should be able to hold about 796 M&Ms. However, since this is type of container is tall and slender, the formula probably over estimates the number of M&M's slightly.

Question: How many M&M's are in a 16 oz jar?

Answer: Using the formula derived in the article, a 160z jar should be able to hold approximately 509 M&Ms.

Question: How many M&M's fit in a 2 1/2 x 2 1/2 x 1 container that holds 1/4 cup?

Answer: Such a container with a volume of 1/4 cup is equivalent to 2 ounces. Based on the formula in the article, a 2oz container should be able to hold about 63 M&Ms.

Question: How many M&M's will fit in test tube that has a 15ml capacity? Its diameter is 16mm, and its height is 100mm.

Answer: First is the fact that an M&M's diameter is about 13mm, which means you don't get an efficient packing arrangement in a 16mm wide tube. In this case, you are essentially "stacking" M&M's up in the tube.

The second thing that makes this tricky is the volume of the test tube. A 15ml test tube should have a volume of 15,000 cubic millimeters. Given the measurements provided, the volume calculates to 20,106.19 cubic millimeters. So either there is additional available volume on in the tube above the 15ml line, or the measurements are for the outside dimensions rather than the inside. Another thing to consider is that the bottom of test tube is curved which means an M&M will not site flat on the bottom.

Nonetheless, using the formula in the article, a test tube should hold about 16 M&M's. However, I happened to have a test tube very similar to the one mentioned in the question. The inner diameter was 15mm, and it held 14 M&M's up to the 15ml line. This is likely due to the issues noted above. Therefore, a standard 15ml test tube should hold 14 M&M's.

Question: How many M&Ms are in 2-1/2 cups?

Answer: There are eight ounces in every cup, so a container that holds 2-1/2 cups has a volume of 20 ounces. Based on the formula from my article, a 20-ounce vessel would contain approximately 637 M&Ms. Therefore, there are 637 M&Ms in 2-1/2 cups.

Question: How many M&M's will fit inside of a 151L wheeled Industrial storage tote?

Answer: This was a pretty specific question, so I looked it up, and indeed Sterilite does make a container this large. This 151L container is also rated for an equivalent 40 gallons. However, for this question, I will stick with the stated volume of 151 liters.

First, we need to convert the volume into milliliters since that is what the formula accepts. 151 liters is equivalent to 151,000 milliliters.

Using the formula in the article, I calculate that this container would hold 161,375 M&M's. However, as noted in the article, the calculation error increases with the size of the container. If this is for a party game (where you need to guess the number of M&M's accurately to win), I will round down to an even number of 160,000 M&M's just to be safe.

Question: How many M&M's will fit in the trunk of a Honda Civic?

Answer: I see you read my other article about stuffing cats into the trunk of a Honda Civic (among other things). In that article, I mentioned that the typical trunk volume of a Honda Civic (at the time) was 12 cubic feet. Since my M&M formulas use ounces or milliliters, we will need to convert cubic feet into something that we can work with.

There are 7.48 gallons in one cubic foot of volume. In addition to this, there are 128 ounces in every gallon.

Therefore, the volume of a Honda Civic trunk is 12 X 7.48 X 128 = 11,489.3ounces

Using the formula in the article, a trunk space of this volume would be able to hold about 362,990 M&M's. However, since the formula tends to over-estimate the number of M&M's a very large container can hold, I would round this value downward. Therefore, I would estimate that the typical Honda Civic trunk could hold about 360,000 M&M's. Now the real challenge comes with trying to fill the trunk without them spilling out!

Question: How many M&M's can fit in a 6" round by 6" tall cylinder?

Answer: By 6" round and 6" tall I assume that you are talking about a cylinder of some kind. Also, it is unknown if the measurements given are the inside or outside dimensions of the cylinder. Assuming these represent the internal measurements, first, we must calculate the volume of the container:

V = piR^2h = (3.1415)X(3)X(3)X(6) = 169.65 cubic inches.

Since 1 cubic inch is 0.55 fluid ounces, the total volume of the cylinder is 169.65 X 0.554 = 94oz.

Using the formula in the article, a 94oz container should be able to hold 2,969 M&M's.

© 2013 Christopher Wanamaker

Comments

XavierJohnson1 on June 29, 2020:

How many regular M&M will fit in a bowl, if a bowl dimensions are-

height 6.5 inches,

width (top of bowl) 6.5 inches,

width(bottom of bowl) 4 inches,

mr man on March 11, 2019:

What type of M&M did the formula work with?

Lisa on December 11, 2018:

how many M&MS would fit in a jar 9 1/2 CM top, 10 1/3rd length and 11CM Bottom

Victoria P on October 18, 2018:

In the first part of the equation where did you get 0.0215?

Larry W Fish from Raleigh on April 07, 2018:

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.

Sunny Kapoor on March 14, 2018:

I have a cylindrical vase 11.75" high and 4.4" in radius. How many M&m would fit in this vase ?

M&M on November 29, 2017:

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.

AT Leung on April 03, 2017:

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.

http://blogs.sas.com/content/iml/2017/02/20/propor...

Will on April 02, 2017:

How many m&m are in a 2lb 10.0 oz bag?

NSJ135 on December 20, 2016:

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

Christopher Wanamaker (author) from Arizona on December 11, 2016:

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

Brendan Harris on December 11, 2016:

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.

Patrick on July 24, 2016:

Nevermind, I see it now.

Patrick on July 24, 2016:

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

Christopher Wanamaker (author) from Arizona on May 07, 2016:

Eric,

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

Eric on May 07, 2016:

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

Robert Morgan from Hutchinson Island, FL - Myrtle Beach, SC - Gilbert AZ on August 06, 2015:

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

Christopher Wanamaker (author) from Arizona on March 31, 2015:

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!

Rebecca Mealey from Northeastern Georgia, USA on March 31, 2015:

"Quesstimation" is an important skill. Love this!

Mary Wickison from Brazil on March 31, 2015:

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

Voted up, and shared.

Christopher Wanamaker (author) from Arizona on February 26, 2015:

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

PDXBuys from Oregon on February 25, 2015:

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

Anne Harrison from Australia on December 09, 2014:

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

Nicu from Oradea, Romania on December 09, 2014:

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

Christopher Wanamaker (author) from Arizona on December 06, 2014:

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.

Eugene Brennan from Ireland on December 06, 2014:

"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?

baranitharan on December 02, 2014:

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

Adam from Overland Park, Kansas on November 30, 2014:

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

Shasta Matova from USA on November 29, 2014:

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.

Liz Elias from Oakley, CA on November 29, 2014:

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

Heidi Thorne from Chicago Area on November 29, 2014:

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!

Paula from The Midwest, USA on November 29, 2014:

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!

PaigSr from State of Confusion on November 29, 2014:

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.

mySuccess8 on November 29, 2014:

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.”)

Patsy Bell Hobson from zone 6a, SEMO on November 20, 2014:

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

Voted up, Pinned

Jayme Kinsey from Oklahoma on November 20, 2014:

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!

Arco Hess from Kansas City, Kansas on October 08, 2014:

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!

Frienderal from Singapore on June 11, 2014:

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!

Christopher Wanamaker (author) from Arizona on May 15, 2013:

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!

calculus-geometry on May 15, 2013:

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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