The Area Of A Sector Calculator
A sector is the wedge-shaped piece of a circle bounded by two radii and the arc between them. Its area is a simple fraction of the whole circle, with the fraction set by the central angle.
Sector area
19.635
- Arc length
- 7.854
- Share of the full circle
- 25.00%
- Full circle area
- 78.5398
- Central angle in radians
- 1.5708
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
sector area = (angle / 360) x pi x r^2, or 0.5 x r^2 x theta in radians
- r
- The radius of the circle
- angle
- The central angle, in degrees
- theta
- The same angle in radians
- sector area
- The wedge-shaped area
How to check the result by hand
- 1
Read the central angle
The angle must be the one at the centre between the two radii, not an angle somewhere on the circle. A 90 degree angle cuts a quarter of the circle.
- 2
Convert to radians if you prefer the short formula
Multiply the degrees by pi and divide by 180. Ninety degrees becomes 1.5707963267948966 radians.
- 3
Compute the full circle area
Pi times the radius squared. For a radius of 5 that is 78.53981633974483, which is the total you are taking a fraction of.
- 4
Take the fraction
Divide the angle by 360 and multiply by the circle area, or use 0.5 times the radius squared times the radians. Either route gives 19.634954084936208.
- 5
Check against the full circle
The sector must be smaller than the whole circle, and the fractions of all your sectors must add to one. A quarter circle of radius 5 is exactly 19.634954084936208.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate The Area Of A Sector page.