Recognizing a Circle Chord Length problem
Chord lengths appear in circular layouts, bolt patterns, arches, surveying, and polygon geometry.
Math calculator
Circle Chord Length Calculator
Find a chord from circle radius and its central angle. Formula and chord length remain visible in one place for independent verification.
Circle Chord Length inputs
Calculation inputs
Why the Circle Chord Length relation holds
A chord subtending angle θ has length 2r sin(θ/2), obtained by bisecting its isosceles central triangle.
Checking Circle Chord Length away from the browser
Bisect the angle and triangle, then apply sine to half the chord over radius.
Radius must be positive and the minor central angle lie from 0° through 180°. The diameter is the 180° chord. If the Circle Chord Length assumptions do not fit, consider segment area.
How to label a Circle Chord Length result
From Circle Chord Length output to working record
Start the Circle Chord Length review with Radius. Compare Radius with its source, then test Central angle in degrees in a second Circle Chord Length run without changing the first Circle Chord Length case.
Independent check for Circle Chord Length
The chord cannot exceed the diameter. For small angles it should approach the corresponding arc length while remaining slightly shorter.
For r=10 and θ=60°, chord length is 20sin30°=10. This Circle Chord Length example can be compared with arc length.
Boundary checks for Circle Chord Length
Sketch Radius before running Circle Chord Length. Place Central angle in degrees on the Circle Chord Length sketch and confirm its unit.
Test a symmetric Circle Chord Length case. In that Circle Chord Length case, compare Central angle in degrees with the expected Circle Chord Length scale.
Rework Circle Chord Length without copying Chord length. Begin with Radius and preserve Central angle in degrees. Predict the scale of the Circle Chord Length answer, then compare it with Chord length. Store a changed Central angle in degrees as another Circle Chord Length case.
A round value for Radius gives Circle Chord Length a quick boundary test. Leave Central angle in degrees fixed, predict Chord length, and compare that prediction with the new Circle Chord Length output. A disagreement identifies a specific part of the Circle Chord Length setup to inspect.
Questions about Circle Chord Length
What is the longest chord?
The diameter.
Is a chord always shorter than its arc?
For a nonzero minor arc, yes.
Why use half the angle?
The radius-to-midpoint line bisects the isosceles triangle.