What Is Arc Length?
An arc is a portion of the circumference of a circle. The arc length is the actual distance you would travel along the curved edge between the two points where a central angle cuts the circle. This calculator finds that distance when you know the circle's radius and the central angle measured in degrees.
How to Use This Calculator
Enter the radius of the circle in any unit (cm, m, inches — the answer comes out in the same unit) and the central angle in degrees, from 0 to 360. The calculator instantly returns the arc length, plus the angle converted to radians and the full circumference for reference.
The Formula Explained
A full circle spans 360 degrees and has a circumference of \(2\pi r\). An arc is simply a fraction of that full circle. The fraction is the angle divided by 360, so:
$$L = \frac{\theta}{360} \times 2\pi r$$
Here \(\theta\) is the central angle in degrees, \(r\) is the radius, and \(\pi \approx 3.14159\). If you already have the angle in radians, the formula simplifies to \(L = \theta \times r\).
Worked Example
Suppose a circle has a radius of 5 units and a central angle of 90 degrees (a quarter circle). The fraction of the circle is \(90/360 = 0.25\). The full circumference is $$2 \times \pi \times 5 \approx 31.4159 \text{ units}.$$ The arc length is $$0.25 \times 31.4159 \approx 7.854 \text{ units}.$$
FAQ
What units does the arc length use? The same unit as the radius you entered. If radius is in meters, the arc length is in meters.
Can the angle be more than 360 degrees? This tool caps the angle at 360 degrees, the full circle. For angles beyond a full turn, subtract multiples of 360 first.
How do I get arc length from radians instead? Multiply the angle in radians directly by the radius: \(L = \theta \times r\). The radians value is shown in the results table.
