Arc Length
Arc Length
Variables
Description
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
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