Circular arcs
turn up frequently in the real world, such as the top of the window shown on the right.
When constructing them, we frequently know the width and height of the arc and need to know the radius.
This allows us to lay out the arc using a large compass.
Given an arc or segment with known width and height:
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.
| ENTER ANY TWO VALUES | ||
| 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.
The width, height and radius of an arc are all inter-related. If you know any two of them you can find the third. For more on this see Sagitta (height) of an arc