Arc Length of a Circle: Formula, Examples & Calculator

The Circle Arc Length Formula

The arc length of a circle is one of the simplest and most useful geometric formulas:

$L = r \cdot \theta$

Where:

• L = arc length
• r = radius of the circle
• θ = central angle in radians

Converting Degrees to Radians

Since the formula requires radians, you’ll often need to convert:

$\theta_{\text{rad}} = \theta_{\text{deg}} \times \frac{\pi}{180}$

Common conversions:

Degrees	Radians
30°	π/6
45°	π/4
60°	π/3
90°	π/2
180°	π
360°	2π

Worked Examples

Example 1: Quarter Circle

Find the arc length of a quarter circle with radius 10 cm.

Solution:

• θ = 90° = π/2 radians
• L = 10 × π/2 = 5π ≈ 15.708 cm

Example 2: Arc with Given Angle

A circle has radius 7 m. Find the arc length subtended by a 120° angle.

Solution:

• θ = 120° = 2π/3 radians
• L = 7 × 2π/3 = 14π/3 ≈ 14.661 m

Alternative Formula (Using Degrees)

If you prefer to work directly with degrees:

$L = \frac{\theta}{360°} \times 2\pi r$

Real-World Applications

• Clock hands: The tip of a clock hand traces a circular arc
• Pizza slicing: Each slice creates a sector with a measurable arc
• Road curves: Highway curves are often designed as circular arcs
• Satellite orbits: Calculating distances along orbital paths

Try It Yourself

Use our Arc Length Calculator to instantly compute circle arc lengths with any radius and angle!