Chord Length Calculator
Find a circle's chord length from the radius plus the central angle, chord height, or apothem.
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 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
Who Can Use This Calculator?
👉 Try our Chord Length Calculator to find any circle's chord length in seconds.