About the Sector Calculator
A sector is a slice of a circle, like a piece of pie, bounded by two radii and an arc. This calculator takes the radius and the angle at the centre and gives the area of the slice, the length of the curved edge, the straight chord across it and the distance all the way round the slice. Type the radius and the angle in degrees and the sector area appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the Sector Calculator
- 1Enter the radius and the angle in degrees.
- 2Pick the units or options from the menus if the sector area tool offers them.
- 3Read the sector area in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the sector area
Designers use it for pie charts, fans, dials and curved garden beds. Carpenters use it for arched windows and curved shelves, and cooks find how much pizza or cake they cut. The result is in whatever unit you used for the radius, squared for areas.
The ratio of the angle to 360° gives the fraction of the circle, which is also the fraction of its area and of its circumference. The calculator shows this fraction as a percentage so you can check your intuition.
How the sector area is worked out
Area = ½ × radius² × angle in radians. Arc length = radius × angle in radians. Chord = 2 × radius × sin(angle ÷ 2). Perimeter = 2 × radius + arc. A sector with a radius of 10 and an angle of 60° has an area of 52.36, an arc of 10.47 and a chord of exactly 10, because a 60° slice makes an equilateral triangle. Its perimeter is 30.47. The full circle would have an area of 314.16, and 60° is one sixth of it.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Angle from 1° to 360°
- Area, arc, chord and perimeter
- Fraction of the circle shown
Mistakes to avoid with sector area
Make sure that the angle is in degrees; for radians multiply by 180 ÷ π first. The chord is the straight line joining the two ends of the arc, and it is shorter than the arc. For angles above 180° the sector is the larger part of the circle, and the formulas still hold.
On phone and computer
On a phone, type into the boxes one after another and read the sector area underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the sector area move. The sector calculator works the same on both. Sectors use angles and circles. Circle Calculator gives the full shape, Angle Converter changes degrees and radians, Trigonometry Calculator finds chord lengths, and Area Calculator handles shapes next to it.
Features
- Fraction = angle ÷ 360
- The chord is shorter than the arc
- Same units for all lengths
- Clear messages when the sector area inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate sector area?
Area = ½ × radius² × angle in radians. Arc length = radius × angle in radians. Chord = 2 × radius × sin(angle ÷ 2). Perimeter = 2 × radius + arc. A sector with a radius of 10 and an angle of 60° has an area of 52.36, an arc of 10.47 and a chord of exactly 10, because a 60° slice makes an equilateral triangle. Its perimeter is 30.47. The full circle would have an area of 314.16, and 60° is one sixth of it.
What is the formula for sector area?
Area = ½ × radius² × angle in radians. Arc length = radius × angle in radians. Chord = 2 × radius × sin(angle ÷ 2). Perimeter = 2 × radius + arc. The sector calculator applies it exactly and rounds only the displayed answer to six significant figures.
What is the difference between arc and chord?
The arc is the curved edge on the circle, the chord the straight line joining its ends.
How do I find the angle if I know the area?
Angle in degrees = 2 × area ÷ radius² × 180 ÷ π, or area ÷ (π × radius²) × 360.
Does it work for a semicircle?
Yes. Use 180°: the area is half the circle and the chord is the diameter.
Is this sector calculator free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.