In a circle, the length of a curved part called an arc depends on the circle's radius.

The formula to find the arc length, which we can call $L$, is:

$$L = r \theta$$

Here's what the letters mean:

• $L$ = arc length
• $r$ = radius of the circle
• $\theta$ = central angle in radians (this is a way to measure angles)

Let’s see an example.

If you have a circle that is 5 cm wide (that’s the radius), and the angle at the center is 1 radian, you can find the arc length like this:

$$L = 5 \times 1 = 5 \text{ cm}$$

This means the arc length is 5 cm.

Understanding this connection is really helpful. As the radius gets bigger, the arc length also gets longer. This is important for figuring out things related to parts of circles, called sectors!