How to find sector area
A sector is a pie-slice of a circle. Its area is the fraction of the full circle swept by the angle: A = (angle ÷ 360) × π × r² for degrees. A 60° sector of radius 6 is (60 ÷ 360) × π × 36 = about 18.85 square units.
The logic is pure proportion. A 60° angle is one sixth of a full turn, so the slice takes one sixth of the circle's total area of about 113.1 square units. The curved edge bounding the sector is measured by the arc length calculator.
How to use this calculator
Enter the radius and the central angle in degrees. A full 360° angle returns the entire circle's area; a 90° angle returns a quarter. The result is in square units of your radius.
Use the radius, not the diameter — halve a measurement taken across the circle first. Because the area depends on r², doubling the radius while keeping the angle fixed quadruples the slice.
Radians and related shapes
For an angle θ in radians, the area is simply A = ½ × r² × θ. To find the curved edge length use the arc length idea; for the whole circle's perimeter use the circle circumference calculator, and for a half-circle the semicircle area calculator.
The two formulas agree because 360° equals 2π radians, so the degree version simplifies to the radian one. Sector areas turn up whenever a slice of a circle needs measuring — a pie chart wedge, a sprinkler's coverage, or a windscreen wiper's swept area.
Frequently asked questions
- What is the formula for sector area?
- A = (angle ÷ 360) × π × r² for degrees, or A = ½ × r² × θ for an angle θ in radians.
- What is the area of a 60° sector with radius 6?
- About 18.85 square units — one sixth of the full circle.
- What angle gives the full circle?
- 360 degrees (or 2π radians) returns the entire circle's area, π × r².
- What units is the sector area in?
- Square units of whatever unit you used for the radius.
- What is the difference between a sector and a segment?
- A sector is bounded by two radii and the arc, like a slice of pie. A segment is the smaller region cut off by a straight chord alone, so its area is the sector area minus the triangle formed by the two radii.