Circle Calculator
Choose radius, diameter, circumference or area as the measure you know, and enter its value. The calculator finds the radius from it and works out the other three measures, rounded to 4 decimal places. Lengths come out in the same unit as your value, and the area in that unit squared. Add a sector angle in degrees or radians to get the sector area, arc length, chord and sector perimeter as well.
How to use the Circle Calculator
- Enter your numbers in the Circle Calculator above.
- Press the Calculate button to see the result.
- To try other numbers, change any value and press the button again.
The circle formulas
d = 2r · · · C = 2πr = πd · · · A = πr² · · · Sector area = (θ / 360) × πr² · · · Arc = (θ / 360) × 2πr
Every formula starts from the radius r. From a diameter the calculator takes r = d / 2, from a circumference r = C / 2π and from an area r = √(A / π). It uses π as 3.141592653589793 and rounds only the figures it shows. Enter 0 or more. A negative value or an empty field gets a message instead of a result. θ is the sector angle in degrees. An angle in radians is a share of 2π instead of 360, which makes the sector area r²θ / 2 and the arc rθ. The chord is 2r × sin(θ / 2), and the sector perimeter is two radii plus the arc.
Worked example
A circle with a radius of 7 cm has a diameter of 14 cm, a circumference of 2π × 7 = 43.9823 cm and an area of π × 49 = 153.938 cm². Start from an area of 100 m² instead and the radius is √(100 / π) = 5.6419 m, the diameter 11.2838 m and the circumference 35.4491 m. Add a sector angle of 90 degrees to the 7 cm circle: the sector area is 153.938 / 4 = 38.4845 cm², the arc length 10.9956 cm, the chord 9.8995 cm and the sector perimeter 24.9956 cm.
Frequently asked questions
Why does π appear in every formula?
π is the ratio of a circle's circumference to its diameter, the same for every circle. The circumference is π times the diameter, and the area is π times the radius squared.
How do I find the area of a sector?
Enter the radius and the sector angle. The sector area is the circle's area times θ / 360. A sector of 90 degrees is a quarter of the circle, and 180 degrees is a semicircle, whose chord is the diameter.
Can I enter the angle in radians?
Yes. Set the angle unit to radians. A radius of 5 and an angle of 2 radians gives a sector area of 25 and an arc length of 10. The angle can be above 0 and up to a full turn, which is 360 degrees or 6.283185 radians.
How accurate are the results?
The calculator uses π as 3.141592653589793 and rounds each figure to 4 decimal places. A very small circle can show an area of 0. A radius of 0.001 has an area of about 0.00000314, which rounds to 0.