Circle sector area calculator
A sector is a slice of a circle between two radii, like a pizza slice. Enter the radius and the angle to get its measurements.
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How to use it
- Enter radius, central angle and length unit.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Area = (θ ÷ 360) × π × r², arc = (θ ÷ 360) × 2πr, perimeter = arc + 2r and chord = 2r × sin(θ ÷ 2).
Example
Inputs: Radius = 10, Central angle = 90 °, Length unit = Centimeters (cm). Result: Sector area: 78.5398 cm²; Arc length: 15.708 cm; Sector perimeter: 35.708 cm.
Limits and caveats
- The angle is in degrees; multiply a radian value by 180 ÷ π first.
- The unit choice only labels the results.
Questions about this tool
What is the formula for the area of a sector?
Multiply the circle area by the angle over 360. A 90° sector with radius 10 is a quarter circle, 78.54.
What is the difference between a sector and a segment?
A sector is bounded by two radii and an arc; a segment is bounded by a chord and an arc only.
How do I find the perimeter of a sector?
Add the arc length to the two radii: arc + 2r.