How this calculator works
Pizza value is area per dollar. Each offer is the number of pizzas multiplied by the area of one pizza, and that total is divided by the offer price. Because the area of a round pizza rises with the square of the diameter, a slightly wider pizza can carry much more food: a 35 cm pizza has 1.36 times the area of a 30 cm one, and a 40 cm pizza has 1.78 times. The comparison assumes the pizzas are the same style and quality; a larger pizza with a thicker base or less topping is not the same food per square centimetre. Use the price per 100 cm2 to see the cost of the pizza itself, and the area per dollar to compare whole deals.
Formula
one pizza area = pi x (diameter / 2)^2. offer area = number of pizzas x one pizza area. area per dollar = offer area / offer price. price per 100 cm2 = offer price / offer area x 100. The best value is the offer with the highest area per dollar.
Worked example
Offer A is one 30 cm pizza for $18: the area is pi x 15^2 = 706.9 cm2, so the area per dollar is 706.9 / 18 = 39.3 cm2 per dollar. Offer B is two 25 cm pizzas for $25: each is pi x 12.5^2 = 490.9 cm2, so the total is 981.7 cm2 and the area per dollar is 981.7 / 25 = 39.3 cm2 per dollar. They are almost exactly equal, even though one offer has twice as many pizzas. A single 35 cm pizza at $22 gives 962.1 / 22 = 43.7 cm2 per dollar and wins.
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Frequently asked questions
Why compare by area and not by diameter?
Area is what you eat. A pizza 10 percent wider has about 21 percent more area, and a pizza twice as wide has four times the area. Comparing diameters makes a large increase in food look small.
Should a thicker pizza count for more?
Yes in practice. A deep pan pizza at the same diameter carries more dough and more food than a thin one. This calculator compares like with like by area; if the styles differ, compare the weight or the number of servings instead.
What about delivery fees and tips?
Add them to the offer price before comparing, because they are part of what the deal costs. A cheaper pizza with a delivery fee can lose to a slightly dearer one collected in person.
How many people does each offer feed?
A 30 cm pizza is commonly cut into 8 slices and feeds two to three hungry adults or three to four with sides. Compare the total area per person, about 250 to 350 cm2 for a main portion, to see whether an offer covers your group.