Enter the arc length and radius into the calculator to evaluate and determine the central angle of the circle contained in that arc. This calculator can also determine the radius or arc length given the central angle and the other variable.

Central Angle Formula

The following equation is used to calculate a central angle contained by a circular arc.

C = L / r
  • Where C is the central angle in radians
  • L is the arc length
  • r is the radius

To calculate a central angle, divide the arc length by the radius. This gives the central angle in radians. To convert to degrees, multiply the result by 57.2958.

Central Angle Definition

A central angle is an angle contained between a radius and an arc length. In other words, the angle of rotation the radius needs to move in order to produce the given arc length.

Central Angle Example

How to calculate a central angle?

  1. First, determine the arc length.

    Measure or calculate the length of the arc.

  2. Next, determine the radius.

    Measure the length of the radius.

  3. Finally, calculate the central angle.

    Using the equation above, calculate the central angle.


What is a central angle?

A central angle is an angle contained by a portion of an arc defined by an arc length and radius. It’s sometimes referred to as the angle of rotation of an arc.

What is an arc length?

An arc length is the measure of the distance along an arc contained by a radius and angle.