Arc Length
Worked example: r = 10 m, quarter turn (90 deg) → 5 pi = 15.70796 m. Press Try an example to run it live, then adjust anything.
Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.
Where Arc Length fits
See also
Circular Sector Area: Both use circle radius and central angle.Circular Segment Area: Both use circle radius and central angle.Area of a Circle: Both use circle radius.Circumference of a Circle: Both use circle radius.Circle Radius from Centre and a Point: Both use circle radius.Sectors and arcs →
Grade 10Grade 10 Math
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Arc Length explained
Arc length is radius times angle, and this little product is no coincidence, it is the very definition of the radian: one radian is the angle whose arc exactly equals the radius. That makes s = rθ the reason radians exist at all. The name was coined around 1870 by James Thomson (brother of Lord Kelvin), but the idea of measuring angles by arc goes back to Roger Cotes in 1714. The relation holds for angles from 0 up to 2π, where the arc becomes the full circumference 2πr. Enter degrees and formula.expert converts them to radians before multiplying.
Engineers lean on this constantly. A highway curve of radius 200 m that turns the road through 30° (0.524 rad) contains 200 × 0.524 ≈ 105 m of pavement; a gear tooth's working surface, a satellite's ground track, and the belt wrap on a pulley are all measured the same way.
Arc Length formula
- = Arc length (m)
- = Radius (m)
- = Central angle (°)
Cite this page
formula.expert. (2026, October 16). Arc Length Formula & Calculator. https://formula.expert/solvers/arc-length
https://formula.expert/solvers/arc-length