About the circular segment calculator
A circular segment is the region between a chord and its arc. It appears in arched windows, tank fill levels and road curves. A common practical problem is finding the radius of an arc you can measure, enter the chord width c and the height h (sagitta) and get r = (c²/4 + h²)/(2h).
Formulas
| Radius from chord & height | r = (c²/4 + h²)/(2h) |
| Area | K = r²(θ − sin θ)/2 |
| Sagitta | h = r(1 − cos(θ/2)) |
| Chord | c = 2r·sin(θ/2) |
Frequently asked questions
How do I find the radius of an arc from its width and height?
r = (c²/4 + h²)/(2h), where c is the chord (width) and h is the height of the arc above it.
What is the area of a circular segment?
K = r²(θ − sin θ)/2, with θ the central angle in radians.