Circle Calculator

A circle is fixed by one measurement. This circle calculator takes the radius, diameter, circumference or area and works out the other three. When you give the radius or diameter, it also shows exact answers in terms of π, such as 25π, alongside the decimal values.

Try:

How to use the circle calculator

  1. Choose which measurement you know.
  2. Enter its value.
  3. Press Calculate to see the radius, diameter, circumference and area.

Formula

C=2πrC = 2\pi r
A=πr2A = \pi r^2

Worked example: Radius 5

  • I know the: Radius
  • Value: 5

✓ Answer checked

r=5,  d=10,  C=10π≈31.415927,  A=25π≈78.539816r = 5,\; d = 10,\; C = 10\pi \approx 31.415927,\; A = 25\pi \approx 78.539816
r = 5
Circle with radius 5 (red) and diameter 10 (dashed).
Step-by-step working (2 steps)

  1. Circumference C = 2πr

    Distance around the circle.

    C=2πr=10π≈31.415927C = 2\pi r = 10\pi \approx 31.415927

  2. Area A = πr²

    Space inside the circle.

    A=πr2=25π≈78.539816A = \pi r^2 = 25\pi \approx 78.539816
Formulas used
d=2rd = 2r
C=2πr=πdC = 2\pi r = \pi d
A=πr2A = \pi r^2
How this was checked
  • ✓ Working back from the area and the circumference gives the same radius.

Frequently asked questions

How do I find the radius from the area?

Divide the area by π and take the square root: r = √(A/π).

How do I find the circumference?

Multiply the diameter by π, or the radius by 2π.

Why give answers in terms of π?

π has infinitely many decimal places, so keeping it as a symbol gives an exact answer.

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