Quick start
- Enter the radius. If you know the diameter, halve it first.
- Optionally enter a sector angle in degrees.
- Read the results as decimals and as multiples of π.
The core formulas
- Diameter: d = 2r
- Circumference: C = 2πr
- Area: A = πr²
For a radius of 7 cm: d = 14 cm, C = 14π ≈ 43.98 cm and A = 49π ≈ 153.94 cm².
Arcs and sectors
A sector is a slice of the circle, like a slice of pizza. Its share of the circle is the angle divided by 360. With r = 7 and a 90° angle, the arc is 90/360 × 14π ≈ 11.00 cm and the sector area is 90/360 × 49π ≈ 38.48 cm².
Example: pizza value
Is one 16-inch pizza more food than two 10-inch pizzas? One 16-inch pizza is π × 8² ≈ 201 square inches. Two 10-inch pizzas are 2 × π × 5² ≈ 157 square inches. The single large pizza is about 28% more food.
Finding the radius from other measurements
From the circumference: r = C ÷ 2π. From the area: r = √(A ÷ π). A circle with an area of 50 has a radius of about 3.99.
Common questions
Why give answers with π?
Exact answers like 49π avoid rounding, and many teachers ask for them.
What value of π is used?
Full calculator precision, about 3.14159265358979.
What units does the area use?
The square of whatever unit the radius is in, such as cm².