Circle Calculator
Solve a circle from radius, diameter, circumference, or area, plus sector area and arc length from a central angle.
Calculate circle measurements
Answer
Area = 78.53981634
- Radius r = 5
- Diameter = 2r = 10
- Circumference = 2*pi*r = 31.41592654
- 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.
- Choose which quantity you know and enter its value.
- The calculator solves for the radius, then the remaining measurements.
- Optionally enter a central angle between 0° and 360°.
- 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.