Arc Length from Chord Length and Radius

The Arc Length a Circle from the Chord and Radius calculator computes arc length of a circle based on the length of a chord (d) on a circle and the radius (r).  

INSTRUCTIONS:  Choose units and enter the following:

• (d) Length of Chord
• (r) Radius of Circle

Arc Length of a Circle (a): The calculator compute the length in meters.  However, this can be automatically converted to other length units via the pull-down menu.

The Math

The formula for the arch length from the length of a chord and radiusis:

   a = 2r⋅sin^-1(d/(2r))

where:

• a is the arc length
• d is the length of the chord
• r is the radius of the circle

Circle 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 an arc of segment 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 cord and the cord's center height.
• Arc Length from Chord and Radius - Computes the arc length of a circle based on the radius and chord length.