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.

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.

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

- Circle definition
- Radius of a circle
- Diameter of a circle
- Circumference of a circle
- Parts of a circle (diagram)
- Semicircle definition
- Tangent
- Secant
- Chord
- Intersecting chords theorem
- Intersecting secant lengths theorem
- Intersecting secant angles theorem
- Area of a circle
- Concentric circles
- Annulus
- Area of an annulus
- Sector of a circle
- Area of a circle sector
- Segment of a circle
- Area of a circle segment (given central angle)
- Area of a circle segment (given segment height)

- Basic Equation of a Circle (Center at origin)
- General Equation of a Circle (Center anywhere)
- Parametric Equation of a Circle

- Arc
- Arc length
- Arc angle measure
- Adjacent arcs
- Major/minor arcs
- Intercepted Arc
- Sector of a circle
- Radius of an arc or segment, given height/width
- Sagitta - height of an arc or segment

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All rights reserved