To calculate the radius

Given an arc or segment with known width and height: Segment of a circle.  A horizontal base line with an arc on the top.  Its height is H and width of the base W The formula for the radius is: where:
W  is the length of the chord defining the base of the arc
H  is the height measured at the midpoint of the arc's base.


See How the arc radius formula is derived.


Height clear
Width clear
Radius clear

Enter any two values and press 'Calculate'. The missing value will be calculated. For example, enter the width and height, then press "Calculate" to get the radius. It works for arcs that are up to a semicircle, so the height you enter must be less than half the width.

Finding the arc width and height

The width, height and radius of an arc are all inter-related. If you know any two of them you can find the third.