Circular Sector Area Calculator

Formula

A = πr²θ/360°

Worked example

With Radius: 5 units, Central angle: 90 degrees, area is 19.634954 square units.

Calculation method

The rule is A = πr²θ/360°.

For this circular sector area example, changing radius from 5 units to 6 units while keeping the other inputs fixed changes area from 19.634954 square units to 28.274334 square units.

Reading area

The central angle determines the fraction of a full 360° circle; sector area and arc length scale by that fraction. In the worked values on this page, radius 5 units, central angle 90 degrees produce area 19.634954 square units.

Practical use

Use it for wedge-shaped surfaces or lengths along a circular edge. The specific task here is to find area from radius, central angle.

Limits and common mistakes

The angle here is in degrees. Arc length follows the curve and differs from straight-line chord length. Verify radius in units before interpreting area; a value measured on another basis would answer a different question.

Why the relationship works

A sector is the fraction of a full circle selected by the central angle. With degrees as input, divide the angle by 360 to obtain that fraction. Multiply full-circle area for a wedge’s area or full-circle circumference for its curved arc length. The straight radial edges are not part of arc length. The circular sector area rule uses radius (units), central angle (degrees) in A = πr²θ/360°; read each symbol as the field named on this page.

Interpreting another set of values

For circular sector area, the fields labeled radius (units), central angle (degrees) are the known quantities. The calculator solves for area in square units using A = πr²θ/360°. A sector area covers a wedge, an arc length follows a curve, and an annulus area covers a ring. Use the output unit to distinguish lengths from surfaces and keep all radii centered on the same circle. When comparing two calculations, keep their units and input definitions identical.

For a second circular sector area check, keep the other default inputs fixed and change radius from 5 units to 7 units. Area changes from 19.634954 square units to 38.48451 square units. This is a comparison of two particular cases. Repeat it near the values relevant to your task; do not assume that every formula changes at a constant rate.

Checks and limits

Confirm the central angle uses degrees rather than radians and that radius is measured from the circle’s center. Arc length is linear, while sector area uses square units. A sector with zero angle has zero arc length and zero area. The reported area is an area. If the input lengths were centimeters, its unit would be square centimeters; the numerical 19.634954 square units therefore describes covering rather than edge length.