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A chord is a straight line segment connecting two points on a circle. The chord length calculator uses the radius and central angle to find both the chord length and the sagitta (the height of the arc above the chord).
Fórmula
c = 2r sin(θ/2); sagitta = r(1 − cos(θ/2))
- r
- radius (length)
- θ
- central angle (radians)
- c
- chord length (length)
- s
- sagitta (arc height) (length)
Guia passo a passo
- 1Chord = 2r × sin(θ/2)
- 2Sagitta = r × (1 − cos(θ/2))
- 3θ is the central angle in radians
- 4Maximum chord is the diameter (θ = 180°)
Exemplos resolvidos
Entrada
r = 10, θ = 60°
Resultado
Chord = 2×10×sin(30°) = 10
Entrada
r = 5, θ = 90°
Resultado
Chord = 2×5×sin(45°) ≈ 7.071
Perguntas frequentes
What is the sagitta?
The sagitta is the perpendicular distance from the midpoint of a chord to the arc. It measures how "tall" the arc is.
When is a chord also a diameter?
When the chord passes through the center of the circle (θ = 180°), it becomes a diameter and equals 2r.
Can I calculate chord length if I know the sagitta and radius?
Yes, rearranging: c = 2√(s(2r − s)).
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