Arc Length

What is this formula?

The arc length formula calculates the distance measured along the curved edge of a circle between two points.

It relates the radius of the circle and the central angle measured in radians.

Arc length is an essential concept in geometry, circular motion, engineering, and physics.

When to use it

Use this formula when:

- Calculating the length of a curved path

- Working with circular geometry

- Analyzing rotating systems

- Solving problems involving wheels, gears, or arcs

- Measuring distances along a circumference

The angle must be expressed in radians for the formula to work directly.

Example

If:

r = 5 m

theta = 1.2 rad

Then:

s = 5*1.2

s = 6 m

Applications

- Geometry and trigonometry

- Mechanical engineering

- Circular motion analysis

- Wheel and gear design

- Architecture and construction

- Robotics and motion systems