⭕ Circle Calculator
Know one measurement of a circle? Enter the radius, diameter, circumference or area to get all the others.
Quick answer: A circle with radius 5 has diameter 10, circumference 2π × 5 ≈ 31.4159 and area π × 5² ≈ 78.5398.
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Circle Calculator inputs
Result
Circle with radius 5
A = 78.5398 sq. units
C = 31.4159
- Radius
- 5
- Diameter
- 10
- Circumference
- 31.4159 (10π)
- Area
- 78.5398 sq. units (25π)
Step by step
- r = 5
- Diameter: d = 2r = 2 × 5 = 10
- Circumference: C = 2πr = 2 × π × 5 = 31.4159
- Area: A = πr² = π × 5² = 78.5398
Circle formulas
Every measurement of a circle depends on a single number – the radius r, the distance from the centre to the edge. Once you know any one of the four values, you can find the rest.
d = 2r · C = 2πr = πd · A = πr²
Working backwards to the radius
| You know | Radius formula |
|---|---|
| Diameter d | r = d ÷ 2 |
| Circumference C | r = C ÷ 2π |
| Area A | r = √(A ÷ π) |
Worked example
A circle has radius 5.
- Diameter: 2 × 5 = 10.
- Circumference: 2 × π × 5 = 10π ≈ 31.4159.
- Area: π × 5² = 25π ≈ 78.5398.
Now go the other way: if a round table top has an area of 1.2 m², its radius is √(1.2 ÷ π) ≈ 0.618 m, so its diameter is about 1.24 m.
Exact answers in terms of π
Teachers often want answers “in terms of π”. When you enter the radius or diameter the calculator shows these too – for r = 5 the circumference is 10π and the area 25π. Multiply by 3.14159… only at the end to avoid rounding errors.
Practical tips
- Measuring a pipe or tree? Wrap a tape around it for the circumference, then use the calculator to get the diameter.
- Pizza maths: a 16-inch pizza has about 1.78 times the area of a 12-inch one, because area grows with the square of the diameter.
- Keep units consistent – circumference comes out in the same unit as the radius, area in that unit squared.
Frequently asked questions
How do I find the radius from the circumference?
Divide the circumference by 2π. A circle with a circumference of 50 cm has radius 50 ÷ 6.283185 ≈ 7.9577 cm.
How do I find the radius from the area?
Divide the area by π and take the square root: r = √(A ÷ π). An area of 100 m² gives r = √31.831 ≈ 5.6419 m.
What is π (pi)?
Pi is the ratio of any circle’s circumference to its diameter – about 3.14159. It is irrational, so its decimals never end or repeat. The calculator uses the full double-precision value.
What is the difference between circumference and area?
Circumference is the distance around the circle (a length, e.g. cm). Area is the surface it encloses (square units, e.g. cm²). Doubling the radius doubles the circumference but quadruples the area.