Calculate circle circumference, radius, diameter and area from one known value, or an arc length from a radius or diameter and central angle. Select mm, cm, m, in or ft; area inputs use matching square units.
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Circle Length Formula
“Circle length” is another name for circumference: the distance around the edge of a circle. Choose one of four known circle values, or use arc mode with a central angle. For an arc, s = rθ, where θ is in radians; equivalently s = r × degrees × Ï€/180.
C = 2πr = πd
r = √(A/π)
r = C/(2Ï€)
d = C/Ï€
A = C²/(4π)
s = rθ (θ in radians)
- C — circle length (circumference)
- r — radius
- d — diameter (d = 2r)
- A — area enclosed by the circle
- π — pi, ≈ 3.14159265
Results use the selected input length unit; area uses the corresponding square unit. Unit changes preserve the same physical quantity. The formulas assume a perfect planar circle, not an ellipse. Arc mode uses a nonnegative central angle; above 360° or 2π radians, the traced path can exceed one circumference. This is not a chord or automatically the shorter arc between two points.
Reference Values
Quick lookup for common radii. Use it to sanity-check the calculator output.
| Radius | Diameter | Length (C) | Area |
|---|---|---|---|
| 1 cm | 2 cm | 6.283 cm | 3.142 cm² |
| 10 cm | 20 cm | 62.83 cm | 314.2 cm² |
| 0.5 m | 1 m | 3.142 m | 0.785 m² |
| 1 m | 2 m | 6.283 m | 3.142 m² |
| 5 m | 10 m | 31.42 m | 78.54 m² |
| 12 in | 24 in | 75.40 in | 452.4 in² |
Common unit conversions for circle length:
| From | Multiply by | To get |
|---|---|---|
| m | 100 | cm |
| m | 3.2808 | ft |
| in | 2.54 | cm |
| ft | 12 | in |
Worked Examples
Example 1 — From radius. A circle has radius 7 cm.
C = 2π(7) = 14π ≈ 43.98 cm.
Example 2 — From diameter. A pipe has a diameter of 4 in.
C = π(4) = 4π ≈ 12.57 in.
Example 3 — From area. A circular pad has area 50 m².
r = √(50/π) ≈ 3.989 m, so C = 2π(3.989) ≈ 25.07 m.
Is circle length the same as perimeter? Yes. For a circle, the perimeter, circumference, and “circle length” all refer to the distance around the boundary.
How accurate is the result? Results use double-precision Ï€ and up to nine significant digits in the display. Scientific notation keeps tiny nonzero answers visible. Open “Calculation details” for formulas and units; displayed numbers are rounded.
