How this calculator works
A price per square inch divides the total price by the flat area in square inches. The usual use is comparing round foods or round materials, where the labelled size is a diameter rather than an area. In diameter mode the page squares the radius, multiplies by pi and converts the result to square inches before dividing the price. The reverse equivalent diameter is found from the area, so a rectangular piece can be described as the round piece with the same area. The table applies the computed rate to common diameters. A round item has more area for the same width than a narrower one, so the area grows with the square of the diameter: doubling the diameter quadruples the area.
Formula
area of a circle = pi x (diameter / 2)^2. price per square inch = total price / area in square inches. total price = price per square inch x area. One square inch is exactly 0.00064516 square metres. The equivalent diameter = 2 x square root(area / pi).
Worked example
A $20 pizza with a 12-inch diameter has an area of 113.10 square inches, so it costs $0.1768 per square inch. At $0.20 per square inch, those 113.10 square inches would cost $22.62. A 16-inch pizza has 201.06 square inches, which is about 78 percent more than the 12-inch one.
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Frequently asked questions
Why compare pizza by area rather than diameter?
Area grows with the square of the diameter, so a 16-inch pizza has about 1.78 times the area of a 12-inch one, not 1.33 times. Comparing price per square inch accounts for that difference when the prices differ.
Does this work for a square or rectangular item?
Yes, in the rate and total modes. Measure the flat area in square inches and enter it. The diameter mode is only for round items because it assumes a circle.
Should the crust count as pizza area?
The formula counts the full circle, crust included. If the crust is thick or uneaten, the edible area is smaller and the value per edible square inch is lower. Use a smaller effective diameter if you want to allow for that.
How do I get square feet instead of square inches?
Divide the square-inch area by 144, or switch the area output selector to square feet. The rate stays per square inch, which is the unit the page calculates.