Circle Calculator

Solve the radius, diameter, area, and circumference of a circle using the calculator below.

Properties of a Circle

A circle is a round, symmetrical shape with no corners or edges where each point along its edge is equidistant from the center. A circle has many properties, such as the radius, diameter, circumference, and area.

The radius is the length of a straight line from the center to the outer edge.

The diameter is the length of a straight line from one edge to the opposite edge, or twice the length of the radius.

The circumference is the distance around the outside, or the perimeter.

The area is the amount of space a circle occupies in a two-dimensional plane.

How to Find the Radius of a Circle

You can find the radius of a circle using one of the following formulas.

Given the Diameter

The radius of a circle is equal to half the circle’s diameter. The following formula defines the radius given the diameter:

r = d / 2

The radius r is equal to the diameter d divided by 2.

Given the Area

If you know the area of a circle, then you can use the inverse of the area formula to find the radius.

r = A ÷ π

The radius r is equal to the square root of the area A divided by pi.

Given the Circumference

If the circumference is known, then you can find the circle’s radius using the formula:

r = C / 2π

The radius r is equal to the circumference C divided by 2 times pi.

How to Calculate the Area of a Circle

You can find the area of a circle using a calculator, or you can use the circle area formula:

A = πr²

The area A is equal to pi times the radius r squared.

How to Find the Circumference

You can find the circumference of a circle using a calculator, or you can use the circumference formula:

C = 2πr

The circumference C is equal to 2 times pi times the radius r.

You can also solve many of these properties for an oval using our ellipse calculator.

Chords and Sectors

A straight line through a circle that does not pass through the center point is called a chord. A chord connects two points on the edge of the circle forming a sector.

A sector is a pie-slice portion of a circle surrounded by two radii that join to the chord and is bounded by the circle’s outer arc.

You can find the area of a sector using the formula:

A = r² × θ / 2

The area A is equal to the radius r squared times the central angle θ in radians, divided by 2.

You can find the chord length using the following formula:

a = 2r × sin(1 / 2θ)

The length of chord a is equal to 2 times the radius r times the sine of 1/2 times the central angle θ.

You can find the arc length using the following formula:

s = rθ

The length arc s is equal to the radius r times the central angle θ in radians.

Unit Circle

The unit circle is a circle with a radius equal to 1, with a center equal to the origin (0, 0). It is used to calculate the cosine, sine, and tangent of any angle within the circle.

The unit circle defines how to find the sides and angles of a right triangle that is formed when extending a line with a known central angle within the circle.

Because the unit circle has a radius equal to 1, the triangle’s hypotenuse is also equal to 1.

The side of the triangle is equal to the sine of the angle, and the base is equal to the cosine.