Arc Length of a Circle

Enter the radius and central angle to compute the length of a circular arc. The result uses the same units as the radius.

Ideal geometric calculation; ensure measurements are accurate.

Examples

r = 5, angle = 60° ⇒ 5.24 units
r = 12 cm, angle = 90° ⇒ 18.85 cm
r = 3 m, angle = 45° ⇒ 2.36 m

FAQ

What angle units are used?

Degrees; convert from radians if necessary.

Can the angle exceed 360°?

Yes. Angles over 360° represent multiple revolutions.

Do radius units matter?

Use any consistent length unit; the result uses that same unit.

Can I input the angle in radians?

Yes. Convert radians to degrees first or adapt the formula.

Additional Information

Formula: L = 2πr × (θ ÷ 360).
Any length unit works as long as you use the same unit for radius and result.
A 360° angle returns the full circumference (2πr).

Connect arc calculations with ISO 80000-2

Arc length relies on radians and carefully presented symbols. Review the ISO 80000-2 article to keep your reports aligned with the standard’s typography and dimensionless quantity guidance.

Go further with plane and solid angles

The radian guide shows how s = rθ emerges directly from ISO 80000 definitions, while the steradian article extends those ideas to beam patterns and photometry. Round out your calculations with the decibel overview if you also chart gain or attenuation alongside geometric motion.