Area of a circular segment calculator
Enter the dimensions of a circular segment and read off its area, its perimeter and the quantities that follow from them.
degrees
Area
7.134 954 1m²
- Perimeter
- 14.925 049
- Chord length
- 7.071 067 8
- Segment height (sagitta)
- 1.464 466 1
Show the working
- Radius = 5
- Central angle = 90
- Area = 5^2 / 2 * (rad(90) - sin(rad(90))) = 7.134 95
- Perimeter = 5 * rad(90) + 2*5*sin(rad(90)/2) = 14.925
- Chord length = 2 * 5 * sin(rad(90)/2) = 7.071 07
- Segment height (sagitta) = 5 * (1 - cos(rad(90)/2)) = 1.464 47
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- area = (r^2 / 2)(theta - sin theta) with theta in radians
- sagitta = r (1 - cos(theta/2))
A segment is the region cut off by a chord — the sector minus the triangle back to the centre.
Lengths are entered in metres by default; switch any field to feet, inches or millimetres and the conversion is exact.