Central Angle Calculator for Arc Length

How to Use This Calculator

This calculator helps you find either the central angle of a circle or the arc length when you know the other parameters. Follow these steps:

1. Enter the radius of the circle in the "Radius (r)" field.
2. Enter either the arc length or the central angle (but not both) in their respective fields.
3. Click the "Calculate" button to get the results.
4. The calculator will automatically calculate the missing value and display both the central angle in degrees and the arc length.

Calculator Formula

The calculator uses the following relationship between arc length (s), radius (r), and central angle (θ in radians):

s = r × θ

From this, we can derive the formula to find the central angle when arc length and radius are known:

θ = s/r

And to find the arc length when radius and central angle are known:

s = r × θ

The calculator converts the angle from radians to degrees for easier interpretation.

Example Usage

Example 1: If a circle has a radius of 5 units and an arc length of 10 units, what is the central angle?

Enter radius = 5 and arc length = 10. The calculator will show that the central angle is 57.296°.

Example 2: If a circle has a radius of 10 units and a central angle of 60°, what is the arc length?

Enter radius = 10 and central angle = 60. The calculator will show that the arc length is 10.472 units.