Circle Calculator: Area and Circumference
Area, circumference, radius and diameter of a circle from any one of them.
Good to know. Pizza maths: one 16-inch pizza has more to eat than two 11-inch pizzas.
How it works
In plain words
The circumference is π times the diameter, or 2π times the radius. The area is π times the radius squared. π is about 3.14159.
The formula
area = π × r² circumference = 2 × π × r = π × d r = C ÷ 2π = √(A ÷ π)
Worked example
A circle with a radius of 5 has an area of π × 5² = 78.539816 and a circumference of 2 × π × 5 ≈ 31.42.
Sources
No outside data or rates: this is plain arithmetic.
4 automated tests check its answers on every change.
About the circle calculator: area and circumference
Every measurement of a circle follows from one number. Give the radius, the diameter, the circumference or the area, and the calculator works out the rest. Use any unit: the lengths come out in the same unit, and the area in that unit squared.
The radius is the distance from the centre to the edge, and the diameter, straight across through the centre, is twice that. The circumference, the distance around, is π times the diameter. The area is π times the radius squared. π, about 3.14159, is the same for every circle.
Because the area grows with the square of the radius, a circle twice as wide has four times the area. That’s why one 16-inch pizza (201 square inches) has more than two 11-inch pizzas (190 square inches together). It also explains why doubling the diameter of a pipe lets four times as much through.
To measure a round object without a ruler across it, wrap a string or tape measure around it for the circumference, then divide by π for the diameter. For the area of a ring, subtract the inner circle’s area from the outer one.
Questions people ask
How do I find the area of a circle?
Multiply π by the radius squared. A radius of 5 gives π × 25 ≈ 78.54.
How do I find the circumference?
Multiply the diameter by π, or the radius by 2π. A diameter of 10 gives about 31.42.
How do I find the radius from the circumference?
Divide the circumference by 2π. A circumference of 100 gives a radius of about 15.92.