Arc Length from Chord Length and Radius

a = 2 r \cdot \sin^{- 1} (\frac{d}{2 r})

$a = 2r*sin^-1(d/(2r))$

(d) Chord Length

$(d)"Chord Length"$

(r) Radius of the circle.

$(r)"Radius of the circle."$

The Math

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

a = 2r⋅sin^-1(d/(2r))

where:

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.