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Circumference Calculator

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Choose what you know about the circle: its radius, diameter, circumference or area. Enter the value and you get the other three, with the formulas and every step.

What do you know?

In any unit: inches give square inches, feet give square feet.

Use a period for decimals, like 12.5. Commas for thousands are fine. The result updates as you type.Decimals with a period, like 12.5

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Result: Area

78.5398

A circle with a radius of 5 has a diameter of 10, a circumference of 31.4159 and an area of 78.5398.

  • Diameter: 10
  • Circumference: 31.4159

Step by step

A = π × 5² = 78.5398

  1. Diameter: d = 2 × 5 = 10.
  2. Circumference: C = 2 × π × 5 = 31.4159.
  3. Area: A = π × 5² = 78.5398.

Formula

d = 2 × r
C = 2 × π × r = π × d
A = π × r² = π × d² / 4
r
radius, from the center to the edge
d
diameter, twice the radius
C
circumference, the distance around
A
area inside the circle
π
pi, about 3.14159

How it works

Every measurement of a circle follows from its radius r, the distance from the center to the edge. The diameter is twice the radius, d = 2r. The circumference, the distance around the circle, is C = 2πr (or πd), and the area is A = πr². Pi (π) is the same for every circle, about 3.14159.

If you know the circumference, divide it by 2π to get the radius; if you know the area, divide by π and take the square root. From the radius the calculator then works out everything else. A circle with a radius of 5 inches has a diameter of 10 inches, a circumference of 31.4159 inches and an area of 78.5398 square inches.

Units carry through: a radius in feet gives a circumference in feet and an area in square feet. For a round table, a pizza or a garden bed, measure across the middle for the diameter. The calculator uses π to full precision, so its results can differ in the last digits from a hand calculation with 3.14. To switch a result between inches and centimeters, use the cm to inches converter.

The formula

Doubling the radius doubles the circumference but makes the area four times as large, because the radius is squared. A 16 inch pizza has (16 / 12)² = 1.78 times the area of a 12 inch pizza.

Pi is the ratio of any circle’s circumference to its diameter. It never ends and never repeats; 3.14 or 22/7 are approximations good to about 2 or 3 digits.

Example

A round table is 4 feet across. What are its circumference and area?

  1. The radius is half the diameter: 4 / 2 = 2 feet.
  2. Circumference: π × 4 = 12.5664 feet.
  3. Area: π × 2² = 12.5664 square feet.

A circle with a diameter of 4 has a radius of 2, a circumference of 12.5664 and an area of 12.5664.

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Frequently asked questions

How do you find the circumference of a circle?

Multiply the diameter by pi, or the radius by 2 × pi. A circle 10 inches across has a circumference of π × 10 = 31.42 inches. With a radius of 3 feet: 2 × π × 3 = 18.85 feet.

How do you find the area of a circle?

Square the radius and multiply by pi: A = πr². A radius of 6 inches gives π × 36 = 113.1 square inches. From the diameter, divide it by 2 first, or use A = πd² / 4.

How do you find the radius from the circumference?

Divide the circumference by 2π (about 6.2832). A circumference of 50 cm gives a radius of 7.96 cm and a diameter of 15.92 cm.

How do you find the diameter from the area?

Divide the area by pi, take the square root to get the radius, and double it. An area of 100 square feet gives a radius of 5.64 feet and a diameter of 11.28 feet.

Last updated: Responsible editor: Jared Alan
Checked against 16 test cases · How we test
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