How to use the chord and segment calculator
Find chord length and segment height of a circle. Enter radius, chord length in the fields above; the half-angle, segment height (sagitta), arc length are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “circle segment”, “bridge arc”, “chord”, “calculate chord and segment”, “find half-angle”.
Formula
Variables
- r — Radius
- c — Chord length
Worked example
With radius = 10, chord length = 12, the calculator gives half-angle ≈ 36.8699 °; segment height (sagitta) ≈ 2; arc length ≈ 12.87002.
Frequently asked questions
What is the chord and segment calculator used for?
Find chord length and segment height of a circle. It helps with questions such as “circle segment”, “bridge arc”, “chord”.
What is the formula for the chord and segment calculation?
Half-angle (°) = asin(c / (2 × r)). Segment height (sagitta) = r-√(r × r-c × c / 4). Arc length = π × r × 2 × [Half-angle] / 180. Here r is radius, c is chord length.
What inputs do I need for the chord and segment calculator?
You need radius, chord length. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the chord and segment calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the chord and segment result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.