Circular segment

Here you can find the set of calculators related to circular segment: segment area calculator, arc length calculator, chord length calculator, height and perimeter of circular segment by radius and angle calculator.

Circular segment

Circular segment – is an area of a “cut off” circle from the rest of the circle by a secant (chord).

On the picture:
L – arc length
h – height
c – chord
R – radius
a – angle

If you know the radius and the angle, you may use the following formulas to calculate the remaining segment values:

Circular segment formulas

Segment area: [1]
Arc length:
Chord length:
Segment height:

If you don’t know the radius and the angle, you can calculate the segment parameters by the chord length and the segment height:

The formula for the segment radius by the chord and the height:

Then, you can calculate the segment angle using the following formula:

You may also use the following calculator to obtain the segment area by its radius and height:

This calculator evaluates the angle by the following formula:
then it uses formula [1] to calculate the segment area.

15 circular segment calculations in one program

Finally, the circular segment calculator below includes all possible calculations regarding circular segment parameters:

  • angle
  • arc length
  • area
  • chord length
  • height
  • radius

Enter two segment parameters, and the calculator will find all the rest.

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