Circular Sector Calculator
From a radius and a central angle, get the area, the arc length, and the chord — the three numbers that describe any pie slice of a circle.
A slice of the whole circle
A sector is the fraction θ/360 of the circle. Enter the radius and the angle and the calculator returns the area, the arc length, and the chord at once.
Angle in degrees, length consistent
The central angle goes in degrees from 0 to 360, and the radius is unit-agnostic — your answers come back in the same length unit (squared for the area).
What is a circular sector?
Two radii and an arc
A circular sector is a "pie slice" of a circle — the region bounded by two radii and the arc between them. It is fixed by two numbers: the radius r, the distance from the centre to the edge, and the central angle θ, the angle at the centre between the two radii. Because a full circle spans 360°, the sector is simply the fraction θ/360 of the whole circle. That makes it the shape behind pizza slices, pie charts, fan-shaped garden beds, windscreen wipers, protractor arcs, and any geometry problem where part of a circle shows up.
Enter the radius and the central angle to get the area, arc length, and chord instantly.
Two formulas come straight from the fraction of the circle the sector covers, plus a third for the chord across its opening.
area = (θ / 360) × π × r²The fraction θ/360 is what makes a sector a slice rather than the whole circle. Multiply that fraction by the circle's full area (π × r²) to get the sector's area, and by the full circumference (2 × π × r) to get the arc length — the curved outer edge. The chord, the straight line across the opening, is 2 × r × sin(θ/2). The arc is always a little longer than the chord because it bows outward.
Suppose you have a sector with a radius of 5 and a central angle of 90° — a quarter circle.
Fraction of the circle
90 ÷ 360 = 0.25 — the sector covers a quarter of the whole circle.
Arc length
0.25 × 2 × π × 5 = 7.853982 — the curved edge, a quarter of the circumference.
Area
0.25 × π × 5² = 0.25 × π × 25 = 19.634954 square units — the space inside the slice.
The three outputs answer three different everyday questions about the slice. The area (about 19.634954 square units for a 90° sector of radius 5) is the surface you cover — the cheese on a pizza slice, the soil in a fan-shaped flower bed, the wedge on a pie chart. The arc length (about 7.853982) is the curved outer edge — the crust along the rounded side of the slice or the path a wiper blade sweeps. The chord (about 7.071068) is the straight line across the opening, connecting the two pointed ends of the arc. The key insight is that the sector is the fraction θ/360 of the whole circle: a 90° angle is a quarter, 180° is a half, and 360° is the full circle, so doubling the angle doubles both the area and the arc length. The chord, by contrast, grows fast at small angles and then flattens out, reaching its longest at 180° (where it becomes the diameter) before shrinking again. Keep the radius in one length unit throughout and the angle in degrees, and every output stays meaningful.
The formulas are exact, but a couple of practical points are worth keeping in mind.
Degrees, range, and consistent units
These formulas describe a perfect, flat sector with the angle measured in degrees from 0 to 360. An angle of 360° is the whole circle; beyond that the shape repeats, so the calculator caps the input there. The radius is unit-agnostic, so the answers are only meaningful if you keep one unit throughout: a radius in centimetres gives an arc length in centimetres and an area in square centimetres, never a mix.