Area of a Circle Arc Segment

This Area of a Circle Arc Segment calculator computes the area of a segment of a circle defined by the radius of the circle (r) and the max distance (h) that the chord reaches away from the edge of the circle. 

INSTRUCTIONS: Choose units and enter the following:

• (r) Radius of Circle
• (h) Depth of Chord from Edge of Circle

Area of a Circle Arc Segment (A): The area (A) returned in square inches.  However, this can be automatically converted to other area units via the pull-down menu.

The Math

The formula for Area of a Circle Arc Segment is as follows: 

A = ½ • r² • (θ - sin(θ))

where 

• A = Area of Circle Arc Segment
• r = radius of the Circle
• θ = angle swept

This calculator uses the formula above with the following substitution:

θ = 2 * acos( (r-h)/r)

where:

• θ = angle in the circle
• r = radius of the circle
• h = max depth of the chord

See Also

A related equation provides the same area if the angle defining the arc chord (θ) is known: To compute the area of the arc segment of a circle using the angle (θ) and radius (r), CLICK HERE.

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