Sector Area Calculator
Find the area of a circular sector from its radius and central angle.
About Sector Area Calculator
The area of a sector is a fraction of the full circle's area, proportional to the central angle.
Formula
Sector Area
A = ½ × r² × θ (θ in radians)
- r
- Radius
- θ
- Central angle in radians
Worked example
With the default values below, Sector Area Calculator returns Sector Area of 78.5398. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Radiusminimum 0 units
- 10 units
- Central Angleaccepts 0–360 °
- 90 °
Results
- Sector Area
- 78.5398 sq units
Step by step
- 1Apply sector area formula= 78.5398
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How is sector area related to circle area?
Sector area = (θ/360°) × πr². It's the proportional slice of the full area.
What is the sector area for a semicircle?
For θ = 180° (π radians): A = ½ × r² × π = πr²/2.