Pizza Dimension

## Pizza Size Comparison - How to compare different size pizzas

Pizza is one of the most beloved foods worldwide, enjoyed by people of all ages. However, one of the most important yet confusing considerations when ordering is the size of the pizza. The standard way to calculate the surface area of a pizza is by using a formula involving the mathematical constant π or Pi (not the pie you can eat!)

Additionally, suppose you want a pizza size comparison of two pizzas (ie. how much larger is this pizza compared to that pizza). In this case, the standard approach is to calculate the area of each pizza and then divide one answer by the other to get the relative difference. However, there is a far more straightforward method! Read on how to become a pizza maths guru! ## Area of a pizza

The Area of a pizza can be calculated in two ways using two similar formulas:

1. The most common equation is Area = πr², where π is a mathematical constant of the ratio of the circumference of any circle to the diameter of that circle (3.14159265359), and r² is the radius of the pizza squared.
2. A second and less commonly used equation is Area = (πd²)/4, where π is multiplied by the diameter squared and then divided by four.

Assuming we had a 10-inch pizza, each equation would look like this.

1. Area =πr² = π x 5² = π x 25 = 78.54 sq inches
2. Area = (πd²)/4 = (π x 10²)/4 = (π x 100)/4 = π x 25 = 78.54 sq inches

## Remove the Pi​

While π is a constant and is required to calculate the area of a pizza, it is not necessary to include it in calculations when comparing the relative size of different pizzas. Let me explain. Using either of the formulas above just before calculating the final area, we can see that it is always a number multiplied by π. For example, a 10″, 12″ and 14″ pizza area calculation could be written like this:

• 10″ pizza area = π x 5²
• 12″ pizza area = π x 6²
• 14″ pizza area = π x 7²

We can drop the π from the equation to determine the relative area of each pizza.

• 10″= 25
• 12″= 36
• 14″ = 49

Therefore the easiest way to compare pizza sizes is by dropping the π and using either the radius or diameter formula. I use either formula, that leaves me with a whole number before I apply the squaring. For example, with a 9″ pizza, I find it easier to square 9 (the diameter) and divide by four (81/4) rather than squaring 4.5 (the radius)(ouch, that makes my brain hurt!)

## An easier comparison

Looking back at the examples above, we can quickly see that a 14′ pizza is almost double the size of a 10″ pizza. (49/25= 1.96)

By applying this method, we can now easily determine each pizza’s relative pizza size comparison or factor. Divide the larger pizza number by the smaller number will yield how many times larger it is. See the table above for pizza sizes 5″ to 25″ for relative size comparisons. Select the large size pizza in the vertical orange column and line it up with the smaller pizza from the grey row at the top. Where the two meet on the table is the factor of how much larger the first pizza is. To compare a 10″ pizza to a 5″ pizza, find 10 in the orange column and move across one to the 5 column. The number in the corresponding box is 4. Therefore a 10 inch pizza is four times the size of a 5 inch pizza.

## How to determine the best value pizza size

Once you have established the relative pizza size comparison, it’s possible to multiply the price of the smaller pizza by the same factor to compare the cost per pizza unit. This will give you an accurate representation of the cost for the same amount of pizza, allowing you to determine which option offers the best value for your money. For example if the 10″ pizza above was \$9 and price of the 5″ pizza was \$3, by applying the 4 times factor (3 x \$4 = \$12) we can see that buying the 10″ pizza is \$3 better value.

Following this process, you can now make an informed decision when choosing which pizza to purchase, ensuring you get the best possible value for your money.

## Summing Up

Understanding how to calculate the area of a pizza is important when ordering and comparing pizza sizes. While π is a valid constant in the area calculation of a round pizza, it is not necessary for a pizza size comparison or to determine pizza value for money.