Arc Length (Radians) Calculator

How it is calculated

Enter the circle's radius r in any length unit and the central angle θ in radians. The arc length is:

s = r × θ

The result is in the same unit as the radius, rounded to two decimals. The radius must be above zero and the angle cannot be negative. No upper limit is applied to the angle, so a value above 2π (about 6.283) simply means the arc wraps around the circle more than once; 7 radians on a radius of 12 gives 84.00. If your angle is in degrees, convert it first with radians = degrees × π / 180.

Common mistakes

• Entering the angle in degrees. Typing 90 instead of 1.5708 gives an arc about 57 times too long.
• Entering the diameter instead of the radius, which doubles the answer.
• Expecting the result in degrees or in angle units. It is a length in the radius's unit.
• Using a negative angle to mean the opposite direction; the tool rejects it, so enter the size of the angle.
• Rounding π to 3 when converting degrees to radians by hand, which makes the arc visibly too short on large radii.