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:
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 fluid ounces.
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.
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.
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 least 98.8% accurate for containers of 1 gallon or smaller
My formula is at least 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 accurate the formulae become.
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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