Arc length

l=\dfrac{\alpha}{360^\circ}\cdot 2\pi r

Result unit: length units

What it describes

The length of the arc corresponding to a central angle

\alpha

l

arc length

\alpha

central angle

[°]

r

radius

An arc is the portion of the circumference proportional to the central angle — a full angle of

360^\circ

gives the whole circumference.

Portions of a circle, central angles, circular motion.

The radius is

r=6

and the central angle is

90^\circ

. Find the arc length.

Substitution

\alpha=90^\circ

r=6

Result

l=\dfrac{90}{360}\cdot2\pi\cdot6=3\pi\approx9.42

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