Circle Calculator (Area, Circumference, Radius and Diameter)

With this circle calculator you enter one value (the radius, diameter, circumference or area) and get the other three right away. It also draws the circle to scale and, with the angle slider, finds the length of an arc, the area of a circular sector and the chord.

Below you will find the formulas, worked examples, a table of values and the most common questions.

How to use the circle calculator

Step 1: Under What do you know, choose whether your value is the radius, the diameter, the circumference or the area. You can also pick a unit.

Step 2: Type the value. A decimal point or comma both work, for example 2.5 or 2,5.

Step 3: For the arc and the sector, drag the angle slider or type the degrees (from 0° to 360°).

Step 4: Click Calculate or press Enter. The drawing and the results update, and the Calculation box shows every step.

Circle formulas

The radius (r) is the distance from the center to the edge. The diameter (d) crosses the circle through the center and equals two radii. The circumference (C) is the perimeter and the area (A) is the surface inside. π is a constant, 3.14159... (the ratio of any circle's circumference to its diameter).

d = 2r    C = 2πr = πd    A = πr²

If you start from something else, solve for the radius first:

r = d ÷ 2    r = C ÷ (2π)    r = √(A ÷ π)

For a sector with angle θ (in radians, θ = degrees × π ÷ 180):

arc = rθ    Asector = r²θ ÷ 2    chord = 2r sin(θ ÷ 2)

Circle examples

Example 1: A circle with radius 5

Once we have the radius we can find the diameter (twice the radius), the circumference and the area:

d = 2 × 5 = 10

C = 2 × π × 5 ≈ 31.42

A = π × 5² = π × 25 ≈ 78.54

The circle has diameter 10, circumference 31.42 and area 78.54.

Example 2: You know the circumference

A circular track is 20 ft around. We solve C = 2πr for the radius and then find the area:

r = 20 ÷ (2 × π) ≈ 3.183

A = π × 3.183099² ≈ 31.83

The radius is 3.183 ft and the track encloses 31.83 ft².

Example 3: You know the area

A round table top has an area of 100 in². We solve A = πr² for the radius and then find the rest:

r = √(100 ÷ π) ≈ 5.642

d = 2 × 5.641896 ≈ 11.28

C = 2 × π × 5.641896 ≈ 35.45

The table is 11.28 in across.

Example 4: Arc and sector for 60°

Take a 60° sector in a circle of radius 6. We convert the angle to radians and use arc = rθ and A = r²θ/2:

θ = 60° × π ÷ 180 ≈ 1.047198 rad

arc = 6 × 1.047198 ≈ 6.283

A = 6² × 1.047198 ÷ 2 ≈ 18.85

The arc is 6.283 long and the sector has an area of 18.85, exactly one sixth of the circle (60° out of 360°).

Table of circles by radius

Values computed with the full value of π and rounded:

Frequently asked questions

How do you find the area of a circle?

Multiply π by the radius squared: A = πr². With radius 4, A = π × 16 ≈ 50.27. If you only have the diameter, divide it by 2 before squaring.

How do you find the circumference from the diameter?

Multiply the diameter by π: C = πd. With diameter 10, C = π × 10 ≈ 31.42.

How do I find the radius if I know the circumference?

Divide the circumference by 2π. With C = 31.4159 the radius is 5 (almost exactly 5).

Which value of π does the calculator use?

The full value your browser stores (3.141592653589793), not 3.14. That is why results can differ slightly from what you get with 3.14 by hand.

How do I find arc length and sector area?

Convert the angle to radians (degrees × π ÷ 180). Arc length is the radius times the angle in radians, and sector area is the radius squared times the angle in radians divided by 2. In the calculator, just drag the angle slider.

Learn more

• Area of a circle
• Circumference of a circle
• Parts of a circle
• Area of a circular sector
• Arc of a circle

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