Arc Length Calculator (Degrees)

How it is calculated

radius is the radius of the circle in any length unit and angle is the central angle in degrees, the angle between the two radii that end the arc.

arc length = (angle ÷ 360) × 2 × π × radius

The factor angle ÷ 360 is the fraction of the full circle the arc covers, and 2πr is the whole circumference. The answer is in the same unit as the radius, and the tool prints just the number, rounded to two decimals, without a unit. Both values must be above zero and the angle can be at most 360°; an angle of 360° returns the full circumference and anything above it, or a zero or negative value, gives no result. The angle must be in degrees, not radians.

Common mistakes

• Entering the angle in radians. An angle of 1.2 rad entered as 1.2 is treated as 1.2 degrees and gives a tiny arc; convert first (1.2 rad is about 68.8°).
• Entering the diameter instead of the radius. The result is then twice as long as the real arc.
• Mixing it up with the chord, which is the straight line between the arc ends. The arc is always longer than its chord.
• Using the angle from the circle's edge (an inscribed angle) instead of the central angle at the centre. The central angle is twice the inscribed one on the same arc.
• Expecting a unit in the answer. The tool does not print one; it is in whatever unit you used for the radius.