`A = 1/2 * "r" ^2 * (2 cos^-1(( "r" - "h" )/ "r" )- sin(2 cos^-1(( "r" - "h" )/ "r" ))`

Enter a value for all fields

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

INSTRUCTIONS: Choose your preferred units and enter the following:

• r - the radius of the circle
• h - the depth from the edge of the circle

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

The Math

The formula for this calculator is as follows: 

                 A = ½ • r² • (θ - sin(θ)                         

where 

• θ = 2 • `cos^(-1)` ( (r-h)/r) in radians.

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.
Related Calculators:

• Circle Area -  This computes the area of a circle given the radius (A = π r²).
• Segment Area f(r,θ) - This computes the area of an arc segment of a circle given the radius (r) and angle (θ)
• Segment Area f(r,h) - This computes the area of an arc segment of a circle given radius (r) and the depth (h) into the circle.
• Sector Area f(r,Θ)- This computes the area of a sector (pie slice) of a circle given the radius (r) and angle (Θ).
• Area of Annulus- This computes the area of an annulus (ring) given the inner radius (r) and outer radius (R).
• Radius -Center to a Point - This computes the radius of a circle given the center point (h,k) and any other point (x,y) on the circle.
• Circumference -  This computes the circumference of a circle given the radius (C = 2 π r).
• Arc Lengths - This computes the length of a cord segment (arc length) on a circle given the radius (r) and angle (Θ)
• Circle within a Triangle -  This computes the radius of a circle inscribed within a triangle given the length of the three sides (a,b,c) of the triangle.
• Circle around a Triangle - This computes the radius of a circle that circumscribes a triangle given the length of the three sides (a,b,c) of the triangle.
• Radius from Circumference - This computes the radius of a circle given the circumference.
• Circumference from Area - This computes the circumference of a circle given the area.
• Radius from Area - This computes the radius of a circle given the area.
• Radius from Chord-  This computes the radius of a circle based on the length of a chord and the chord's center height.