# You Got Science in My Peanut Butter!

It is a well-established candy-scientific fact that peanut butter and chocolate are two great tastes that taste great together. But not all combinations are equal. I have long held the opinion that the regular size Reese’s Peanut Butter Cup is superior in tastitude to the miniature size. You might disagree, but maybe you have also noticed a difference.

Why should there be a difference? Maybe the shape plays a role: the miniatures are taller than the regulars, but are barely half the diameter. But could it also be that the chocolate to peanutbutter ratio is different for these different sizes? To Science!

I obtained two regular and two miniature Reese’s peanut butter cups and weighed each using a scale I borrowed from a friend. I then carefully separated the chocolate from peanut butter using only my hands and a dull knife, weighing each portion separately. This was easier than you might think, and I believe this experiment could easily be done with kids to encourage curiosity. It involves both dissecting and candy!

Now I suspected there would be a difference from inspecting the nutritional information for the two sizes. For roughly the same serving size, the regular cups have more sodium and protein while the minis have more calories and sugars. Since peanut butter contains salt and protein I thought the regular cups might have more peanut butter than the minis.

Just how much more was pretty surprising: the regular cups are 46% peanut butter by weight, while the minis are only 33% peanut butter. The rest is chocolate. This might explain why someone people prefer the regular and others the minis: I like the creamier, saltier regulars more than the sweet minis.

An interesting aside: while the regular cups are manufactured in Hershey, PA, the minis are made in Mexico.

So in a sphere of radius r, volume is in r^3, and surface in r^2. In Reese’s candies, peanut butter should scale roughly as the volume of the cup, and chocolate as its surface. My question is as follows: is the increase in the ratio peanut butter/chocolate consistent with this expectation? I can imagine that the engineers at Reese had to increase the height of the chocolate layer to increase the integrity of the candy as the size of the cup increases.

Bastien, in my experiment I only considered weight, but we could also consider volume. If we consider a Reese’s cup it is more cylindrical than spherical. The heights of the regular and mini cups are 1.3 and 1.55 cm, respectively. If we take the radius to be the average of the radii at the top and bottom surfaces, then they are 2.275 and 1.3 respectively. The using the formula pi * radius^2 * height for the volume of a cylinder, we get 21.14 and 8.23 cubic centimeters respectively. This ratio of mini : regular is 0.389. The ratio of the peanut butter masses alone is 0.26. Since I did not measure actual volume, it could either be because there is proportionally more peanut butter in the regulars, or because the peanut butter in the regulars is heavier. Possibly both. But I think that the top and bottom layers of chocolate are actually thinner in the bigger regular size, contrary to your expectations.