A full circle’s circumference is just a special case of an arc — this finds the length of any portion of a circle’s edge, swept out by a given angle.
How it works
Converting the angle from degrees to radians and multiplying by the radius gives the arc length.
What this does not include
This does not include chord length (the straight-line distance between the arc’s two endpoints) — this calculator measures the curved distance along the arc itself, not the straight-line shortcut across it.
How to use this calculator
- Enter the radius and the angle in degrees.
A worked example
A circle with radius 10 and a 90° central angle: arc length = (angle/360) × 2πr = 15.707963.
What the variables mean
| Variable | Meaning |
|---|---|
| Radius | Distance from the circle’s center to its edge |
| Angle | Central angle spanning the arc, in degrees |
Edge cases worth knowing
A 360° angle gives the full circumference — the arc length formula naturally reduces to 2πr at that angle, since the “arc” becomes the entire circle.
A radius of zero collapses every arc to length zero regardless of angle, so the calculator declines to show a result.
Frequently asked questions
What happens at exactly 360 degrees?
The arc length equals the full circle’s circumference — a 360-degree “arc” is the entire circle.
Why convert degrees to radians first?
Because the arc length formula (radius times angle) mathematically requires the angle in radians, the natural unit relating angle to arc length on a unit circle.
What’s a practical use for arc length?
Estimating material needed for a curved section of trim, a curved road or track segment, or any partial-circle boundary.
