Circle Sector Calculator
Sector area, arc length and chord from a radius and an angle.
Sector area, arc length and chord from a radius and an angle. A sector is the pizza slice: the region between two radii and the arc joining them.
Sector area (units²)
78.5398
Arc length 15.708 units · 25% of the circle
Arc length is rθ and area is r²θ⁄2, both with the angle in radians — 90° is 1.5708 radians. The chord is the straight line across the opening, which is shorter than the arc; here 14.1421 against 15.708.
How the Circle Sector Calculator works
A sector is the pizza slice: the region between two radii and the arc joining them. Its area is r²θ⁄2 and its arc is rθ, both with the angle in radians. The chord (the straight line across the opening) is always shorter than the arc, and this shows both.
Also known as: area of a sector · sector of a circle calculator · pie slice area calculator · sector area formula
Where to go next
The Circle Sector question rarely arrives on its own. These are the ones that usually come with it:
- Circle Calculator — Area, circumference, radius and diameter from any one of them.
- Arc Length Calculator — Arc length and chord, with the radian conversion shown.
- Volume Calculator — Six shapes, with the litre conversion built in.
- Percentage Calculator — Every common percentage question in one place.
Frequently asked questions
How do I find the area of a sector?
Take the fraction of the full circle the angle represents and apply it to the circle's area. A 90° sector is a quarter circle, so a radius of 10 gives a quarter of 100π, or 78.54 square units.
What is the arc length of a sector?
The radius times the angle in radians. A 90° angle is π⁄2 radians, so a radius of 10 gives an arc of 15.71 units.
What is the difference between an arc and a chord?
The arc is the curved edge; the chord is the straight line between its endpoints. The arc is always longer, and the gap widens as the angle grows.
How do I convert degrees to radians?
Multiply by π and divide by 180. A full circle is 2π radians, a half circle π, and a right angle π⁄2.
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