# How to Measure the Arc of a Circle

To calculate the length of a circular arc (l), multiply the angle in radians (α) by the radius of the circle (r). $$ l = \alpha \cdot r $$

**Example**

Let's calculate the length of a circular arc (l).

The angle is π/3 (which is 60°) and the circle has a radius of r = 5 cm.

The arc length is 5.23 cm.

$$ l = \alpha \cdot r $$ $$ l = \frac{\pi}{3} \cdot 5 \ cm $$ $$ l = \frac{3.14 \cdot 5}{3} \ cm $$ $$ l = 5.23 \ cm $$

**Note**: The angle must be in radians. If the angle is given in degrees (e.g., 60°), convert it to radians before applying the formula.

**Proof**

The proof is quite simple.

An angle measured in radians is the ratio of the arc length (l) to the radius of the circle (r):

$$ \alpha = \frac{ l }{ r } $$

With a straightforward algebraic manipulation, we find the arc length in terms of the radius and the angle:

$$ l = \alpha \cdot r $$

This demonstrates one of the practical benefits of using radians to measure angles.

And so forth.