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Circumference Calculator

Calculate the circumference, diameter, radius, or area of any circle — enter any one value and all three others update instantly.

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What Is the Circumference of a Circle?

The circumference of a circle is the distance all the way around its edge — the circle’s equivalent of a perimeter.

If you could cut a circle’s edge and straighten it into a line, that line would be the circumference.

Circumference Formulas

There are two equivalent formulas, depending on what you know:

Using the radius (r):

C = 2πr

Using the diameter (d):

C = πd

Both give the same result because the diameter is twice the radius (d = 2r). The constant π ≈ 3.14159265 is defined as the ratio of any circle’s circumference to its diameter — C ÷ d = π, always.

How to Find Radius, Diameter, or Area from Circumference

If you know the circumference C:

You wantFormula
Radiusr = C ÷ (2π)
Diameterd = C ÷ π
AreaA = C² ÷ (4π)

If you know the area A:

You wantFormula
Radiusr = √(A ÷ π)
Diameterd = 2√(A ÷ π)
CircumferenceC = 2√(π × A)

Worked Examples

Example 1 — from radius: A circle has a radius of 7 cm.

  • Diameter: d = 2 × 7 = 14 cm
  • Circumference: C = 2π × 7 ≈ 43.98 cm
  • Area: A = π × 7² ≈ 153.94 cm²

Example 2 — from circumference: A circle has a circumference of 100 inches.

  • Radius: r = 100 ÷ (2π) ≈ 15.915 in
  • Diameter: d = 100 ÷ π ≈ 31.831 in
  • Area: A = 100² ÷ (4π) ≈ 795.77 in²

Example 3 — from area: A circle has an area of 50 ft².

  • Radius: r = √(50 ÷ π) ≈ 3.989 ft
  • Diameter: d ≈ 7.979 ft
  • Circumference: C = 2√(π × 50) ≈ 25.066 ft

Sources

Frequently Asked Questions

What is the circumference of a circle?

The circumference is the total distance around the outside of a circle — its perimeter. For a circle with radius r, the circumference is C = 2πr ≈ 6.2832 × r. For a circle with diameter d, the circumference is C = πd ≈ 3.1416 × d.

What is the formula for circumference?

There are two equivalent formulas. Using the radius: C = 2πr. Using the diameter: C = πd. Both give the same result because d = 2r. π (pi) is the mathematical constant approximately equal to 3.14159265.

How do you find the circumference from the diameter?

Multiply the diameter by π: C = π × d. For example, a circle with a diameter of 10 inches has a circumference of π × 10 ≈ 31.416 inches. This relationship (C = πd) is in fact the original definition of π — the ratio of circumference to diameter.

How do you find the radius from the circumference?

Divide the circumference by 2π: r = C ÷ (2π). For example, if the circumference is 44 cm, the radius is 44 ÷ (2 × 3.14159) ≈ 7.003 cm. You can also find the diameter by dividing by π: d = C ÷ π.

What is the relationship between circumference and area?

Both depend on the radius. Area = πr² and Circumference = 2πr, so Area = C² ÷ (4π). Conversely, C = 2√(π × A). For example, a circle with area 78.54 in² has a circumference of 2√(π × 78.54) ≈ 31.42 in.