About Pizza Calculations

Pizza Calculations is a very simple web app for you to compare the relative size difference between two pizzas or any circular objects.

Formula

$$ \left( \frac{\text{Big pizza}}{\text{Small pizza}} \right)^2 $$

Why?

The area of a circle is given by \(\pi R^2\). To compare the areas of two pizzas, we use the following formulas:

\(A_1 = \pi R^2\) and \(A_2 = \pi r^2\)

Therefore, the ratio of the areas is \(\frac{A_1}{A_2}\), where \(A_1 \geq A_2\):
$$\frac{\pi R^2}{\pi r^2} = \frac{\cancel{\pi} R^2}{\cancel{\pi} r^2} = \frac{R^2}{r^2} = \boxed{{\left(\frac{R}{r}\right)}^2} $$
This formula also yields the correct ratio when the diameter, instead of radius, is used on both sides, since the diameter is simply \(\frac{1}{2}D\) and the \(\frac{1}{2}\) on the top and bottom cancel out:
$$ \frac{R^2}{r^2} = \frac{(\frac{1}{2}D)^2}{(\frac{1}{2}d)^2} = \frac{(\cancel{\frac{1}{2}}D)^2}{(\cancel{\frac{1}{2}}d)^2} = \frac{D^2}{d^2} = \boxed{{\left(\frac{D}{d}\right)}^2} $$

Tips

• If you don't eat the crust, subtract the \(\text{crust width} \times 2\) from the diameter.
• If both fields are set to the same unit, you can use whatever unit you want (\(mm\), \(ft\), \(m\), etc.) and still end up with the right calculation.
• It is probably easier to remember the simple formula \(\left( \frac{\text{Big pizza}}{\text{Small pizza}} \right)^2\) than to remember the page's address.