Geometry

Circle Calculator

Solve a circle from radius, diameter, circumference, or area, plus sector area and arc length from a central angle.

Calculate circle measurements

r
Answer
Area = 78.53981634
  1. Radius r = 5
  2. Diameter = 2r = 10
  3. Circumference = 2*pi*r = 31.41592654
  4. Area = pi*r^2 = 78.53981634

How to use the circle calculator

Enter any one of radius, diameter, circumference, or area and the calculator recovers the other three. Add a central angle to also get the sector area and arc length.

  1. Choose which quantity you know and enter its value.
  2. The calculator solves for the radius, then the remaining measurements.
  3. Optionally enter a central angle between 0° and 360°.
  4. Read the sector area and arc length for that angle.

Formula or method

Area = pi r^2; circumference = 2 pi r; sector area = (angle/360) pi r^2; arc length = (angle/360) 2 pi r.

Worked examples

Circle from radius

Problem: r = 5

Solution: Area = 25pi ≈ 78.54 and circumference = 10pi ≈ 31.42.

Sector from a central angle

Problem: r = 5, angle = 90°

Solution: Sector area = (90/360) * pi * 5^2 ≈ 19.63; arc length ≈ 7.85.