Chord Calculator (Circle)
Free chord calculator for circles. Enter radius plus angle, sagitta, distance to the chord, or arc length to get chord length, arc length, and areas instantly.
What do you know?
Same unit for all fields
Degrees
Formula: c = 2r sin(θ/2)
Chord computed from the selected known values.
How to use / Methodology
Select the combination of known values you have on the circle, then enter the numbers into the matching panel. We derive the chord length using standard trigonometric geometry so the output is immediate and precise even if you switch from degrees to arc lengths.
We always compute the central angle first (in radians) and use that to derive every other result: chord length, arc length (r×θ), triangle area (½r² sin θ), and segment area (½r²(θ − sin θ)). The calculators for sagitta, distance to chord, and arc length all convert their inputs back to that same central angle before reporting the rest of the metrics.
Why this tool stands out
Most “chord calculators” online are for music theory (identify a chord from notes). This one is tailored to circle geometry as used in engineering, architecture, CAD, and construction. You can enter any combination of radius + angle, sagitta, distance to chord, or arc length. Every tab shows the same segment metrics (chord, arc, triangle area, segment area) so you can compare scenarios quickly.
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 the radius, then enter that value.
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. The validator catches those edge cases.
Full original guide (expanded)
Related geometry tools
Tip
If your angle is already in radians, enter it through the arc-length tab (L = rθ) or convert it to degrees before using the “Radius + Angle” tab.