Pi and Pie

Here’s Mathematical Proof It’s Always Better to Buy the Larger Pizza

Unfortunately, NPR's study does not take toppings into account.
Unfortunately, NPR’s study does not take toppings into account. Photo: Joe Gough / Shutterstock

“Eat more pizza to save more money” might sound like the economic advice of a broke college student, but it’s actually mathematically sound advice. According to an extensive review of 74,476 pie prices from 3,678 pizzerias around the country plotted out by NPR, even a two-inch difference in pizza size matters quite a bit. While the price difference between small, medium, and large pies is typically a matter of a few dollars, the total surface area of those pizzas almost always increases significantly with the larger sizes.

Case in point: A 12-inch pizza is really twice as much pizza (2.3 times, to be exact) as its eight-inch counterpart, not simply four inches more. An even better deal would be — if you’re hungry — to spring for the 16-inch pizza, which at first purports to be twice as large as an eight-inch pie, but is in reality actually four times as large, and only a few dollars more. To see this pizza-area magic as a function of price, NPR’s Planet Money has set up a graph with a sliding bar here that allows you to play around with the data.

Just remember, this bit of life-hack-esque math applies only to circular pies — sorry, Sicilian lovers — the area of which, if you recall from sixth-grade math*, increases with the square of the radius multiplied by pi, the mathematical constant. Now all we need is for someone to prove, hopefully, that this price-per-surface-area rule carries over to the cost of toppings.

74,476 Reasons You Should Always Get The Bigger Pizza [Planet Money/NPR]

*Circumference: C=πd or cherry-pie-delicious as mnemonic; Area: A=πr2 or apple-pies-are-too.

Here’s Mathematical Proof It’s Always Better to Buy the Larger Pizza