# Sector Area Calculator

> Work out the area of a circle sector from the radius and either the central angle or the arc length, with the angle, arc and perimeter.

Category: Algebra, geometry & advanced math · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/sector-area-calculator

A sector is a pie slice of a circle. Its area is the same fraction of πr² as its angle is of a full turn, or simply ½ × radius × arc length.

Also called: Circle sector calculator.

## Inputs
- I know (options: Radius and angle, Radius and arc length; default angle)
- Radius (default 6)
- Central angle (default 90)
- Angle in (options: Degrees, Radians; default deg)
- Arc length (default 6)
- Length unit (options: Millimetres (mm), Centimetres (cm), Metres (m), Kilometres (km), Inches (in), Feet (ft), Yards (yd), No unit (plain numbers); default cm)

## Results
- Sector area
- Arc length
- Sector perimeter (2r + arc)
- Central angle
- Central angle in radians
- Share of the full circle

## Formula

```
Area = (θ/360°) × πr² = ½r²θ (θ in radians) = ½ × r × s;  s = rθ
```

Where:
- r: radius
- θ: central angle
- s: arc length

## Worked example
1. 90° is 90/360 = 25% of the circle.
2. Area = 0.25 × π × 6² = 9π ≈ 28.274334 cm².
3. Arc = 0.25 × 2π × 6 = 3π ≈ 9.424778 cm.

**Result:** A quarter circle of radius 6 cm has an area of about 28.27 cm².

## What the result means

Use it for pie-chart slices, fan-shaped rooms, sprinkler coverage or a slice of a round cake. Doubling the radius quadruples the area at the same angle.

## Assumptions and limits
- The sector is cut from a perfect circle by two radii.
- The arc cannot be longer than the full circumference, and the angle cannot exceed 360°.
- For the area between the arc and its chord, use the segment area on the arc length calculator.

## Questions

### What is the difference between a sector and a segment?

A sector is bounded by two radii and the arc (a pie slice). A segment is bounded by a chord and the arc.

### Why is area ½ × r × arc?

A sector behaves like a triangle with base equal to the arc and height equal to the radius, just as a circle’s area is ½ × r × circumference.

## Related calculators
- [Arc Length Calculator](https://calculators.geekmidst.com/calculators/arc-length-calculator)
- [Circle Calculator](https://calculators.geekmidst.com/calculators/circle-calculator)
- [Area Calculator](https://calculators.geekmidst.com/calculators/area-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/sector-area-calculator