Radius of an arc or segment



A formula and calculator are provided below for the radius given the width and height of the arc. Definition: The radius of an arc or segment is the radius of the circle of which it is a part.A formula and calculator are provided below for the radius given the width and height of the arc.

Try this Drag one of the orange dots to change the height or width of the arc. The calculated area is shown.



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.

To calculate the radius

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.



Derivation

See How the arc radius formula is derived.

Calculator

ENTER ANY TWO VALUES Height clear Width clear Radius clear Calculate 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. For more on this see Sagitta (height) of an arc

Using a compass and straightedge

Other circle topics

General

Equations of a circle

Angles in a circle

Arcs

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