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

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The Area of an Arc Circle formula, A = ½• r²•  (θ - sin(θ)), computes the area defined by               A = f(r,θ)          A = f(r,h)  an arc and the chord connecting the ends of the arc (see blue area of diagram).  

INSTRUCTIONS: Choose units and enter the following:

• (r)  - This is the radius of the circle.
• (θ) - This is the angle defining the arc. 

Area of an Arc Segment of a Circle (A):  The calculator returns the area (A) in square meters.  However the user can automatically convert the output units to numerous other compatible units via the pull-down menu.

Related Calculators

• A = f(r,h) - Compute the area of an Arc Segment of a Circle based on the radius (r) and depth (h)

See Also

If `theta` is unknown, the same area can be calculated if the depth (h) from the edge of the circle toward the center is known.  (See figure) The following equation calculates the area using r and h:
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.