Circle Sector Calculator

How it is calculated

A sector is the slice of a circle between two radii. The tool first finds the fraction of the full circle that the slice covers: f = angle / 360, with the angle in degrees (not radians). Then it scales the whole circle: area = f × π × r2 and arc = f × 2 × π × r, where r is the radius. The area comes out in square units of the radius you entered and the arc length in the same linear unit. Both results are rounded to two decimals. The radius and the angle must be greater than zero, otherwise no result is shown. Angles above 360 are accepted and simply give a fraction larger than one, which wraps around the circle more than once.

Common mistakes

• Typing the angle in radians (for example 1.047) while the tool expects degrees, which yields a tiny sector.
• Entering the diameter instead of the radius, which makes the area four times too large and the arc twice as long.
• Confusing arc length with the straight chord between the two ends; the arc is always longer.
• Forgetting that the area is in square units and the arc in plain units, then adding the two together.
• Entering the angle of the remaining part of the circle (for example 300 instead of 60).