What is the Pizza Slice Calculator?
This calculator treats a pizza as a perfect circle and splits it into n equal wedge-shaped slices. Each slice is a circular sector. Given the pizza's radius and the number of slices, it computes the area of one slice (how much pizza you actually get) and the length of crust along the outer edge of each slice (the arc length).
How to use it
Enter the pizza's radius in centimetres — that's half the diameter, so a 40 cm pizza has a radius of 20 cm. Then enter how many equal slices you're cutting. The result shows the area per slice, the crust (arc) length per slice, the cutting angle, and the total area of the whole pizza.
The formula explained
The total area of a circle is \(\pi r^{2}\). Dividing it among n equal slices gives each slice an area of:
$$\text{Slice Area} = \frac{\pi \cdot \text{Radius}^{2}}{\text{Slices}}$$The crust is the outer arc of each sector. The full circumference is \(2\pi r\), so each slice's crust is:
$$\text{Crust Length} = \frac{2\pi \cdot \text{Radius}}{\text{Slices}}$$The angle of each wedge is simply:
$$\theta = \frac{360^{\circ}}{\text{Slices}}$$
Worked example
For a pizza with radius 20 cm cut into 8 slices: total area = \(\pi \times 20^{2} = 1256.64 \text{ cm}^{2}\). Each slice:
$$\frac{1256.64}{8} = 157.08 \text{ cm}^{2}$$Crust per slice:
$$\frac{2 \times \pi \times 20}{8} = 15.71 \text{ cm}$$Each slice spans:
$$\frac{360^{\circ}}{8} = 45^{\circ}$$
FAQ
Do I use radius or diameter? Use the radius — half of the diameter. A 30 cm diameter pizza means radius = 15 cm.
Why does crust length grow with radius? The outer edge is part of the circle's circumference, which is proportional to the radius, so a bigger pizza gives more crust per slice.
Does this work for any sector, not just pizza? Yes. Any equal division of a circle into n parts follows the same sector-area and arc-length formulas.
