Which pizza is actually the better deal?
Pizza is sold as a whole pie, but you eat it by the area. That mismatch is where the interesting math lives. A pizza's size is quoted as a diameter — 12-inch, 16-inch, and so on — yet the amount of food you get grows with the square of that diameter. This calculator turns each pizza's diameter and price into a price per square inch, then tells you which one gives you more pizza for your money.
The formula
A pizza is a circle, so its surface area is:
Area = π × (diameter ÷ 2)²
Then value is simply price divided by area:
Price per square inch = price ÷ area
The pizza with the lower price per square inch is the better deal. Comparing per-square-inch prices — rather than sticker prices or diameters — is the only apples-to-apples way to judge two different sizes.
Why bigger pizzas are usually cheaper per bite
Because area depends on the diameter squared, small increases in width produce large increases in food. Widen a pizza by a third and you get roughly three-quarters more pizza:
- 10-inch: π × 5² = 78.5 sq in
- 12-inch: π × 6² = 113.1 sq in
- 14-inch: π × 7² = 153.9 sq in
- 16-inch: π × 8² = 201.1 sq in
- 18-inch: π × 9² = 254.5 sq in
A 16-inch pizza has about 78% more pizza than a 12-inch (201.1 ÷ 113.1 = 1.78), even though it is only 33% wider. So the large is the better buy as long as it costs less than 78% more than the medium. It also means two 12-inch pizzas (226.2 sq in total) give you slightly more pizza than one 16-inch (201.1 sq in) — handy when a shop runs a two-for-one deal on mediums.
A worked example
Suppose a 12-inch pizza costs $14.00 and a 16-inch costs $19.00. The 12-inch works out to $14.00 ÷ 113.1 = $0.124 per square inch, while the 16-inch is $19.00 ÷ 201.1 = $0.094 per square inch. The 16-inch is about 24% cheaper per square inch, so it is clearly the better value even though it costs $5 more up front.