Sector Area Calculator
The area of a slice of a circle from its radius and angle, with the arc length and the perimeter of the slice.
A sector is a fraction of a circle, and the fraction is the angle over 360°.
How the sector area calculator works
A sector is a fraction of a circle, and the fraction is the angle over 360°. So a 60° sector is a sixth of the disc, and its area is πr² × (60 ÷ 360). The arc length follows the same fraction of the circumference, and the perimeter of the slice is that arc plus the two straight radii — the part people forget when ordering edging.
Formula: square a²; rectangle ab; triangle ½bh; circle πr²; parallelogram bh; trapezoid ½(a+b)h; ellipse πab
Worked examples
| Inputs | Area | Note |
|---|---|---|
| Radius 10, angle 60° | 52.3599 | 52.36 — a sixth of the circle |
| A quarter circle | 50.2655 | 50.27 |
| A 30° pie slice | 37.6991 | 37.70 |
FAQFrequently asked questions
What is a sector?
A slice of a circle bounded by two radii and the arc between them — a pie slice.
What is the formula?
πr² × (angle ÷ 360) in degrees, or ½r²θ in radians.
What is the perimeter of a sector?
The arc plus two radii — not just the arc, which is the usual mistake.
What is the difference between a sector and a segment?
A segment is cut off by a straight chord; a sector is bounded by two radii and reaches the centre.
How do I work in radians?
A full turn is 2π radians, so 60° is π/3. The area is then ½r²θ.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.