Chord Calculator (Circle)
This is a geometry chord calculator (not a musical chord finder). Pick what you know — radius & angle, radius & sagitta, radius & distance from center, or arc length — and we’ll calculate the chord length and other segment properties.
Same unit for all
Degrees
Formula: c = 2 r sin(θ/2)
Chord formulas used
1. From radius and central angle (θ in radians): \(c = 2r \sin \left(\frac{\theta}{2}\right)\)
2. From radius and central angle (θ in degrees): \(c = 2r \sin \left(\frac{\theta \pi}{360}\right)\)
3. From radius and sagitta s: \(c = 2 \sqrt{2rs - s^2}\)
4. From radius and distance from center d: \(c = 2 \sqrt{r^2 - d^2}\)
5. Segment area: \(A = \frac{1}{2} r^2 (\theta - \sin \theta)\)
Why this page is better than “chord” music tools
Most “chord calculators” online are for music theory (identify a chord from notes). This one is specifically for circle geometry as used in engineering, architecture, CAD, and construction, similar to OmniCalculator’s chord length tool — but we also show the segment area and triangle area, which many sites don’t.
FAQs
What is sagitta?
Sagitta (sometimes “rise” or “segment height”) is the height from the chord up to the arc.
Can I use diameter instead of radius?
Yes. Just divide the diameter by 2 to get radius, then enter that.
Why am I getting “invalid input”?
Some inputs are geometrically impossible, e.g. a sagitta bigger than the radius, or a center-to-chord distance bigger than the radius.