Chord Length Calculator

Find a circle's chord length from the radius plus the central angle, chord height, or apothem.

R chord apothem h α

Chord Length Calculator

A chord is a straight line segment connecting two points on a circle's edge. Our Chord Length Calculator finds its length from the radius plus whichever related measurement you have — the central angle, the chord height (sagitta), or the apothem.

Chord Length Terms Explained

Central Angle (α): the angle formed at the circle's center by the two radius lines drawn to the chord's endpoints.
Chord Height (h) — also called the sagitta — the perpendicular distance from the midpoint of the chord to the nearest point on the arc.
Apothem: the perpendicular distance from the circle's center to the chord itself.

Chord Length Formulas

From Central Angle: c = 2R·sin(α ÷ 2)
From Chord Height: c = 2√(2Rh − h²)
From Apothem: c = 2√(R² − apothem²)

Example Calculations

From Central Angle: R = 10, α = 100°

c = 2 × 10 × sin(50°) ≈ 15.32

✓ Chord Length ≈ 15.32

From Chord Height: R = 10, h = 3.21

c = 2√(2 × 10 × 3.21 − 3.21²) ≈ 15.32

✓ Chord Length ≈ 15.32

From Apothem: R = 10, apothem = 6.43

c = 2√(10² − 6.43²) ≈ 15.32

✓ Chord Length ≈ 15.32

Features of Our Chord Length Calculator

✅ Supports three different known values
✅ Labeled diagram for quick visual reference
✅ Instant, accurate results
✅ Free to use, no sign-up required

Who Can Use This Calculator?

Students & Teachers – For geometry and trigonometry homework
Engineers & Architects – For arches, bridges, and curved structures
Machinists & Fabricators – For laying out curved cuts and parts
Woodworkers & DIYers – For arcs, curves, and circular layouts

👉 Try our Chord Length Calculator to find any circle's chord length in seconds.