What is the Pizza Size Calculator?
Pizza is sold by diameter, but you actually eat the area. Because area grows with the square of the diameter, a pizza that looks only a little bigger can hold far more food. This calculator takes the diameters of two round pizzas and tells you each one's surface area, the ratio between them, and how much more (or less) food the first pizza gives you.
How to use it
Enter the diameter of Pizza A and Pizza B in inches (use any consistent unit — the ratio is the same). Press calculate to see both areas in square inches, the area ratio, and the percentage difference. Pair it with the price of each pizza to find the best value per square inch.
The formula explained
A round pizza is a circle, so its area is \(A = \pi \times (d/2)^2\), where d is the diameter. To compare two pizzas you divide one area by the other; the \(\pi\) cancels, leaving \(\text{ratio} = (d_1/2)^2 / (d_2/2)^2\), which simplifies to \((d_1/d_2)^2\). Subtract 1 and multiply by 100 to get the percentage of extra food.
$$\frac{A_A}{A_B} = \frac{\pi\left(\frac{\text{Diameter A}}{2}\right)^2}{\pi\left(\frac{\text{Diameter B}}{2}\right)^2} = \left(\frac{\text{Diameter A}}{\text{Diameter B}}\right)^2$$
Worked example
Compare a 16-inch pizza (A) with a 12-inch pizza (B). Area A = \(\pi \times 8^2 = 201.06\ \text{in}^2\). Area B = \(\pi \times 6^2 = 113.10\ \text{in}^2\). Ratio = \(201.06 / 113.10 = 1.78\), meaning the 16-inch pizza has about 78% more food than the 12-inch — often making one large cheaper per slice than two smalls.
FAQ
Does the unit matter? No. As long as both diameters use the same unit, the ratio and percentage are identical; only the area figures change.
Why is a bigger pizza such a better deal? Area scales with the square of diameter, so a 20% larger diameter means about 44% more pizza — but the price rarely rises that fast.
Does crust thickness matter? This tool compares flat surface area only. Thicker crust or deep-dish pies add volume not captured here.
