How this calculation works
For a fixed chord, a shallower minor arc gives a larger radius. A sagitta equal to half the chord describes a semicircle.
THE FORMULA
R = c²/(8h) + h/2A worked example
A chord of 8 with a rise of 2 belongs to a circle of radius 5.
Good to know
Measure the sagitta perpendicular to the chord.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Recover the radius of a circular arc from its chord and midpoint rise.
The primary result is labeled “Circle radius”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Measure the sagitta perpendicular to the chord.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
A chord of 8 with a rise of 2 belongs to a circle of radius 5.
Which rule does this calculator apply?
R = c²/(8h) + h/2