How to Figure Cost Per Square Inch of Pizza

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posted on 17 years ago — updated on 1 second ago

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When deciding where to order a pizza, you likely want to consider value. One way to consider the value of a pizza is to determine how much the pizza costs per square inch. In order to find this cost, you need to determine the area of the pizza, which can be found by using basic formulas. As long as you know the price and dimensions of the pizzas, you can find out which restaurant offers the best value.

Steps

Finding the Per Inch Cost of a Round Pizza

Set up the formula for the area of a circle. The formula is A = π ( r 2 ) {\displaystyle A=\pi (r^{2})} A=\pi (r^{{2}}) where r {\displaystyle r} r equals the length of the circle’s radius.

Divide the size of the pizza in half. Pizza sizes are measured by their diameter. To find the length of the radius, you have to divide the diameter in half. For example, if you are ordering a 20 inch pizza, calculate 20 ÷ 2 = 10 {\displaystyle 20\div 2=10} 20\div 2=10. So the radius of the pizza is 10 inches.

Plug the length of the radius into the formula. Remember to substitute for the variable r {\displaystyle r} r. For example, if the radius is 10 inches, your formula will look like this: A = π ( 10 2 ) {\displaystyle A=\pi (10^{2})} A=\pi (10^{{2}}).

Square the length of the radius. To square a number, multiply it by itself. For example, if the radius is 10 inches, you would calculate 10 × 10 = 100 {\displaystyle 10\times 10=100} 10\times 10=100, so your formula will now look like this: A = π ( 100 ) {\displaystyle A=\pi (100)} A=\pi (100).

Multiply by π {\displaystyle \pi } \pi . You can use a calculator, or use 3.14 for π {\displaystyle \pi } \pi . The result will give you the area, in square inches, of your pizza. For example: A = π ( 100 ) {\displaystyle A=\pi (100)} A=\pi (100) A = 3.14 ( 100 ) {\displaystyle A=3.14(100)} A=3.14(100) A = 314 {\displaystyle A=314} A=314So, the area of a 20-inch round pizza is 314 square inches.

Divide the price of the pizza by the number of square inches. This will give you the cost per square inch of the pizza. For example, if a pizza costs $32 and has an area of 314 square inches, you would calculate 32 ÷ 314 = .101 {\displaystyle 32\div 314=.101} 32\div 314=.101. So, the cost per square inch of pizza is about .10, or 10 cents.

Compare the value of pizzas. When comparing value, the best value is the pizza with the lowest cost per square inch. This is only true, however, when comparing pizzas with the same toppings. A cheese pizza is likely to be cheaper per square inch than a pizza with several toppings, but that doesn’t necessarily make it the best value.

Finding the Per Inch Cost of a Rectangular Pizza

Set up the formula for the area of a rectangle. The formula is A = l × w {\displaystyle A=l\times w} A=l\times w where l {\displaystyle l} l equals the length of the rectangle, and w {\displaystyle w} w equals the width of the rectangle.

Find out the length and width of the pizza. Usually menus will only give you one measurement. You will have to contact the restaurant and ask if they will provide you with the length and width of the pizza. If it is a square pizza, the length and width will be the same. For example, you might want to find the value of a square 16-inch pizza. Both the length and the width will be 16 inches.

Plug the length and width of the pizza into the formula. Due to the commutative property of multiplication, It doesn’t matter which dimension you use for the length and which you use for the width. For example, for a square 16-inch pizza, your formula will look like this: A = 16 × 16 {\displaystyle A=16\times 16} A=16\times 16.

Multiply the length and the width of the pizza. This will give you the area of the pizza in square inches. For example: A = 16 × 16 {\displaystyle A=16\times 16} A=16\times 16 A = 256 {\displaystyle A=256} A=256So, the area of a square 16-inch pizza is 256 square inches.

Divide the price of the pizza by the number of square inches. This will give you the cost per square inch of the pizza. For example, if a pizza costs $32 and has an area of 256 square inches, you would calculate 32 ÷ 256 = .125 {\displaystyle 32\div 256=.125} 32\div 256=.125. So, the cost per square inch of pizza is about .13, or 13 cents.

Compare the cost per square inch of different pizzas. The pizza with the lowest cost per square inch will have the best value. However, you should only compare similar types of pizzas when looking for the best value (for example, two veggie pizzas). A pizza with fewer toppings will cost less per square inch than a pizza with several toppings, but that doesn’t necessarily make it the best value.