Circle Area & Circumference Calculator

A circle is a plane figure made up of all points at the same distance from a center point. Its size — both area and circumference — can be determined from the radius alone.

Enter the radius to calculate both the area and the circumference of a circle. Useful for calculating circular site areas or solving math problems.

For example, a circle with radius 5 cm has an area of about 78.54 cm² and a circumference of about 31.42 cm.

Circle Area & Circumference Calculation Method

S: area, L: circumference, r: radius

Area: 0

Perimeter: 0

About This Calculator

A circle is the set of points at a fixed distance from a centre, and two constants — π and the radius — determine everything about it. Area grows with the square of the radius, while circumference grows in direct proportion.

Enter the radius, diameter, circumference or area to have the other values calculated.

A circle is fully determined by its radius: circumference 2πr and area πr². A radius of 5 gives 31.42 and 78.54, and doubling the radius quadruples the area rather than doubling it. Archimedes bounded π between 223/71 and 22/7, accurate to about two decimal places, using polygons inscribed in and around the circle.

Key Formula:Area = πr² · Circumference = 2πr = πd

Frequently Asked Questions

What is the difference between radius and diameter?

The radius is the distance from the centre to the edge; the diameter runs all the way across through the centre, so diameter = 2 × radius. Circle problems often give one and expect the other.

How do I find the area from the circumference?

Divide the circumference by 2π to get the radius, then use πr². A circle with a circumference of 31.4 cm has a radius of 5 cm and an area of about 78.5 cm².

What is the difference between the radius and the diameter?

The radius runs from the centre to the edge while the diameter runs right across, so the diameter is twice the radius. Formulas normally use r, so halve a given diameter before substituting.

How do I find the area of a sector?

Multiply the full area by the fraction of the circle: (angle / 360) × πr². A 60° sector of radius 6 is one sixth of 113.10, which is 18.85.

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Sources & last update

2026-10-19