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Area of a Circular Segment given its height
Definition: The number of square units it takes to fill a segment of a circle
Try this Drag one of the orange dot that defines an endpoint of the segment. Adjust the segment height. Note the number of square units it takes to fill it and the calculation.

If you know the radius of the circle and the height of the segment, you can find the segment area from the formula below. The result will vary from zero when the height is zero, to the full area of the circle when the height is equal to the diameter. where:
r  is the radius of the circle of which the segment is a part.
h  is the height of the segment.

Note: The result of the cos-1 function in the formula is in radians.

Another method

If you know the central angle of the segment (the angle subtended by the segment at the center of the circle) you can use the method Area of a circular segment given the central angle.

Applications

This calculation is useful as part of the calculation of the volume of liquid in a partially-filled cylindrical tank. For more on this see Volume of a horizontal cylindrical segment.

Calculator

Use the calculator below to calculate the segment area given the radius and height of the segment, using the formula described above

Radius
Segment height
Area
 
 

Make sure you are using the same units for both measurements.

Other circle topics

General

Equations of a circle

Angles in a circle

Arcs