Why pizza size is a geometry problem
Pizzas are sold by diameter, but you eat their area, and area grows with the square of the diameter. An 18-inch pizza is only 1.5 times as wide as a 12-inch one, yet it covers 2.25 times as much. That is why one large pizza is often a better deal than two mediums, even when the price looks similar. This calculator compares two orders by total area and price per square inch.
The formulas
- Area of one pizza = π × (diameter ÷ 2)²
- Total area of an order = number of pizzas × area of one pizza
- Price per square inch = total price ÷ total area
- Pizzas of size A that equal one of size B = (diameter B ÷ diameter A)²
Worked example: two 12-inch pizzas or one 18-inch
Order A: two 12-inch pizzas for $25.98. Order B: one 18-inch pizza for $21.99.
- Area of a 12-inch pizza: 3.1416 × 6² = 113 sq in, so order A gives 226 sq in.
- Area of an 18-inch pizza: 3.1416 × 9² = 254 sq in.
- Price per square inch: $25.98 ÷ 226 = $0.115 for A, $21.99 ÷ 254 = $0.086 for B.
- Order B gives 12.5% more pizza and costs 24.8% less per bite.
- One 18-inch pizza equals 2.25 twelve-inch pizzas.
Area by diameter
| Diameter | Area | Equal to … 12-inch pizzas |
|---|---|---|
| 10 in | 79 sq in | 0.69 |
| 12 in | 113 sq in | 1.00 |
| 14 in | 154 sq in | 1.36 |
| 16 in | 201 sq in | 1.78 |
| 18 in | 254 sq in | 2.25 |
| 20 in | 314 sq in | 2.78 |
What the area does not tell you
- Crust. The outer inch or so is crust. Its share is larger on a small pizza: on a 10-inch pie, a 1-inch rim takes 36% of the area, on an 18-inch pie only 21%. If you skip the crust, the large pizza wins by even more.
- Toppings. Shops do not always scale toppings with area, so a large pizza can be thinner on cheese. Compare the menu descriptions.
- Square and rectangular pizzas. Multiply length by width instead of using the diameter. A 12 × 16 inch sheet pizza has 192 sq in, close to a 16-inch round.
- Variety. Two mediums let you order two different pizzas; the calculator shows what that choice costs.
How much pizza per person
A common estimate is two to three slices per adult, or about 75 to 110 sq in each. For eight people that is roughly 600 to 900 sq in: three 18-inch pizzas, or five to six 14-inch ones. Teenagers and big appetites eat more, young children about half.