Pythagorist
Geometry

Circle Calculator

Enter any one circle measurement — radius, diameter, circumference or area — and instantly calculate all the others. Full step-by-step working shown using π. Ideal for GCSE maths and beyond.

Radius

7

Diameter

14

Circumference

43.9823

Area

153.938

How it works

  1. Given radius

    r=7r = 7

    Starting with radius r = 7.

  2. Diameter

    d=2r=2×7=14d = 2r = 2 \times 7 = 14

    Diameter = 2 × radius = 14.

    Result:d = 14

  3. Circumference

    C=2πr=2π×7=43.9823C = 2\pi r = 2\pi \times 7 = 43.9823

    Circumference = 2π × 7 = 43.9823.

    Result:C = 43.9823

  4. Area

    A=πr2=π×72=153.938A = \pi r^2 = \pi \times 7^2 = 153.938

    Area = π × 7² = 153.938.

    Result:A = 153.938

Circle formulas

C=2πr=πdA=πr2d=2rC = 2\pi r = \pi d \qquad A = \pi r^2 \qquad d = 2r
rrRadius — distance from centre to edge
ddDiameter — distance across the circle through the centre
CCCircumference — the perimeter of the circle
AAArea — the space inside the circle

Example substitution

r=5⇒d=10,  C=2π(5)≈31.42,  A=π(5)2≈78.54r = 5 \Rightarrow d = 10, \; C = 2\pi(5) \approx 31.42, \; A = \pi(5)^2 \approx 78.54

From radius 5: diameter = 10, circumference ≈ 31.42, area ≈ 78.54.

Worked examples

A circle has radius 6 cm. Find its area and circumference.

  1. 1
    Area: A = π × 6² = 36π ≈ 113.10 cm²
  2. 2
    Circumference: C = 2π × 6 ≈ 37.70 cm
Answer: A ≈ 113.10 cm², C ≈ 37.70 cm

A circle has circumference 44 cm. Find its radius.

  1. 1
    Formula: C = 2πr
  2. 2
    Rearrange: r = C ÷ (2π)
  3. 3
    Calculate: r = 44 ÷ 6.2832 ≈ 7.00 cm
Answer: r ≈ 7.00 cm

A circle has area 78.54 cm². Find its radius.

  1. 1
    Formula: A = πr²
  2. 2
    Rearrange: r = √(A/π)
  3. 3
    Calculate: r = √(78.54/π) ≈ 5.00 cm
Answer: r ≈ 5.00 cm

Frequently asked questions

What is the area of a circle?+

Area = πr². If you know the diameter, use r = d/2 first.

What is the circumference of a circle?+

Circumference = 2πr = πd.

What is π (pi)?+

Pi (π) is the ratio of a circle's circumference to its diameter. π ≈ 3.14159265358979...

How do you find the radius from the area?+

Rearrange A = πr² to get r = √(A/π).

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