Arc Length and Chord Calculator
Find the arc length, chord, sagitta and apothem of a circular arc from its radius and central angle.
units
degrees
Length along the curved arc
- 1
Angle to radians
60 × π ÷ 180 = 1.047198All circular formulas use radian measure. - 2
Arc length
r × θ = 10 × 1.047198 = 10.4720
How does this calculator work?
For a circular arc with radius r and central angle θ, convert θ to radians, then arc length is r·θ, chord is 2r·sin(θ/2), sagitta is r(1−cos(θ/2)), and apothem is r minus the sagitta. All lengths use the same unit as the radius.
Formula
How this is calculated
Enter the radius r of the circle and the central angle θ in degrees. The angle is first converted to radians with θᵣ = θ · π / 180, because every circular formula below uses radian measure.
The arc length is the distance travelled along the curved edge: L = r · θᵣ. The chord is the straight line joining the two endpoints of the arc: c = 2r · sin(θᵣ / 2). The sagitta h = r(1 − cos(θᵣ / 2)) is the perpendicular height from the midpoint of the chord to the arc, and the apothem d = r − h is the distance from the circle centre to the chord.
All lengths share the same unit as the radius, and the angle uses degrees on input. The radius must be positive; a zero or negative radius is rejected. At θ = 0 every length is zero, and at θ = 360° the chord and sagitta collapse while the arc equals the full circumference 2πr.
Frequently asked questions
The arc length follows the curved path of the circle, while the chord is the straight line connecting the two endpoints. The chord is always shorter than the arc for any non-zero angle.
The sagitta is the height of the arc — the perpendicular distance from the midpoint of the chord to the highest point of the arc. It is computed as h = r(1 − cos(θ/2)).
Enter the central angle in degrees; the calculator converts it to radians internally using θᵣ = θ · π / 180 before computing each length.
Also known as
TG we-Calculate Editorial Team. (2026). Arc Length and Chord Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/arc-length-chord-calculator
TG we-Calculate Editorial Team. "Arc Length and Chord Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/arc-length-chord-calculator.
TG we-Calculate Editorial Team, "Arc Length and Chord Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/arc-length-chord-calculator
@misc{wecalculate_arc_length_chord_calculator, title = {Arc Length and Chord Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/arc-length-chord-calculator}}, year = {2026}, note = {TG we-Calculate} }
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