You need to figure out three important things to come up with an accurate guess:
The volume of the container
The volume of a single M&M
The packing fraction for jars filled with M&Ms
In determining the volume of a single M&M, you can use the water displacement method or with the aid of a vernier caliper.
The ellipsoid formula will also give an accurate answer to the actual volume of one M&M candy.
While the volume of each regular M&M varies, you can settle with .636 cubic centimeters - the volume used by Ira Flatow, host of NPR's Talk of the Nation Science Friday.
We know that 12 oz is equivalent to 354.882 cm³. Use this Ounces to Cubic Centimeters Converter.
A limit of how many M&Ms would fit is: 558 (354.882 / .636).
But because M&Ms wouldn't pack that densely, that many would not fit. The packing fraction for jars filled with M&Ms plays a very important role in this part.
According to this paper: Improving the Density of Jammed Disordered Packings Using Ellipsoids, the packing fraction is 66.5%.
So, there would fit (558 * 0.665) 370 M&Ms.
Red or green? Milk chocolate or peanut? Mega or mini? You may know your favorite color and variety of M&M's, but there’s still a lot you probably don’t know about the candy that melts in your mouth, not in your hand. Here are a few colorful facts to snack on shared by Mentalfloss.com.