Arc Length Formula
Calculate the length of a curved section of a circle.
Used in engineering, construction, and geometry problems.
The Formula
s = rθ (radians) or s = (θ/360) × 2πr (degrees)
Arc length is the distance along a curved section of a circle. Using radians makes the formula beautifully simple — just multiply the radius by the angle.
Variables
| Symbol | Meaning |
|---|---|
| s | Arc length (same units as radius) |
| r | Radius of the circle |
| θ | Central angle (in radians or degrees) |
Example 1
Find the arc length for a 60° angle on a circle with radius 10 cm
s = (60/360) × 2π × 10
s = (1/6) × 62.83
s ≈ 10.47 cm
Example 2
An angle of π/4 radians on a circle with radius 8 m
s = r × θ = 8 × π/4
s = 2π ≈ 6.28 m
When to Use It
Use the arc length formula when:
- Calculating the length of curved roads or tracks
- Measuring distances along circular paths
- Designing gears, pulleys, and circular components
- Converting between angle measure and distance along a curve