GeomBench

Sector Area Calculator

What fraction of the full circle's pie are you slicing?

Radius

Angle (°)

Sector area

28.274

Arc length: 9.425

What you entered

Radius: 6Angle: 90°

1
Fraction of the full circle
90 ÷ 360= 0.25
2
Sector area
0.25 × π × 6²= 28.2743
3
Arc length
0.25 × 2π × 6= 9.4248

Result

Sector area: 28.274

A 90° slice of a circle with radius 6 has an area of 28.274 and an arc length of 9.425.

Sector area and arc length for a radius of 5

A sector is a slice of a circle. Both area and arc length scale directly with the angle, as a fraction of the full 360 degrees.

Radius	Angle	Sector area	Arc length
5	30 deg	6.54	2.62
5	45 deg	9.82	3.93
5	60 deg	13.09	5.24
5	90 deg	19.63	7.85
5	120 deg	26.18	10.47
5	180 deg	39.27	15.71
10	90 deg	78.54	15.71

Everything is linear in the angle: 90 degrees gives exactly three times the area of 30 degrees, and 180 degrees gives a semicircle at half the full 78.54. The last row shows the difference between the two inputs - doubling the radius at a fixed 90 degrees quadruples the area but only doubles the arc length, because area depends on the radius squared and arc length on the radius itself. A 180 degree sector at radius 5 and a 90 degree sector at radius 10 happen to share an arc length of 15.71 while their areas differ by a factor of two.

It's just a fraction of the circle

A sector is the fraction (angle ÷ 360°) of a full circle. Multiply that fraction by the full circle's area (πr²) for sector area, or by its circumference (2πr) for arc length.

Where sectors show up

Pizza-slice portions, pie charts, sprinkler coverage patterns, and gear-tooth design all rely on sector area and arc length calculations.

Frequently asked questions

How do I calculate the area of a sector?

In degrees: Area = (θ/360) × π × r². In radians: Area = ½ × r² × θ. A sector with radius 10 and angle 90°: Area = (90/360) × π × 100 = 78.54. That's exactly ¼ of the full circle.

How do I find arc length?

In degrees: Arc = (θ/360) × 2πr. In radians: Arc = r × θ. A 60° arc on a circle with radius 12: Arc = (60/360) × 2π × 12 = 12.57. Arc length is the curved distance along the circle's edge.

How do I convert between degrees and radians?

Radians = degrees × (π/180). Degrees = radians × (180/π). Common conversions: 90° = π/2, 180° = π, 360° = 2π, 45° = π/4, 60° = π/3, 30° = π/6.