How this calculator works
The area of a round pizza is pi times the square of its radius, so the area grows with the square of the diameter. A 30 cm pizza carries 2.25 times the area of a 20 cm pizza for the same shape, which is why up sizing is often better value than adding a second small pizza. If you leave the crust, the part you eat is the area inside the crust ring, and a thick crust removes much more than it looks: on a 30 cm pizza a 2 cm crust removes about a quarter of the area. The price per area puts different sizes and different shops on the same footing.
Formula
area = pi x (diameter / 2)^2. edible area = pi x (diameter / 2 - crust)^2 when the crust is left. area per slice = edible area / 8. price per 100 cm2 = price / edible area x 100. price per slice = price / 8.
Worked example
A 30 cm pizza has a radius of 15 cm and an area of pi x 225 = 706.9 cm2. With a 2 cm crust left uneaten, the edible area is pi x 13^2 = 530.9 cm2, a quarter less. At $18 the price is 18 / 530.9 x 100 = $3.39 per 100 cm2, and each of 8 slices carries 66.4 cm2 and costs $2.25. A 40 cm pizza has 1256.6 cm2, about 78 percent more area for the same price.
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Frequently asked questions
Is a larger pizza always better value?
Usually, if the price rises more slowly than the area. The area rises with the square of the diameter, so a pizza 33 percent wider has 78 percent more pizza. Put the actual prices into the comparison and let the price per area decide.
How many slices are in a pizza?
This page assumes 8 slices and lets you compute the area and price for one. A 12 inch pizza is often cut into 8 slices, a 16 inch into 8 or 12, and a party pizza into squares. The slice count changes the size of a slice, not the total area.
Does a thick crust change the answer much?
Yes if you do not eat it. The crust is a ring, and its area is the outer circle minus the inner circle. On a smaller pizza the same crust width takes a larger share of the whole, because the ring is a bigger fraction of a smaller circle.
Why does the price per slice differ from the price per area?
The price per slice assumes equal slices, while the price per area is the pure value measure. If you share a pizza with people who eat different amounts, the price per area is the fairer comparison between pizzas.