Arc Length Calculator
Use this calculator to find the length of an arc in a circle using radius and central angle.
What Is Arc Length?
Arc length is the distance along the curved edge of a circle between two points. Unlike a straight line (called a chord), arc length follows the curve itself. If you imagine walking around the edge of a pizza slice crust, the distance you walk is the arc length.
Arc length is used in geometry, engineering, architecture, robotics, physics, and everyday design. Anytime a part is curved rather than straight, arc length is often the right measurement to use.
Arc Length Formula
When angle is in radians
The cleanest formula is:
s = rθ
- s = arc length
- r = radius of the circle
- θ = central angle in radians
When angle is in degrees
If your angle is in degrees, use:
s = (θ / 360) × 2πr
This version comes from taking the fraction of the full circle and multiplying by the full circumference.
How to Use This Length Arc Calculator
- Enter the radius of the circle.
- Enter the central angle.
- Select whether the angle is in degrees or radians.
- Click Calculate Arc Length.
The calculator will return:
- Arc length
- Equivalent angle in radians and degrees
- Circle circumference
- What percent of the full circle your arc represents
Worked Examples
Example 1: Degrees
Radius = 10 cm, angle = 90°.
Arc length = (90/360) × 2π(10) = 5π ≈ 15.708 cm.
Example 2: Radians
Radius = 8 m, angle = 1.2 radians.
Arc length = rθ = 8 × 1.2 = 9.6 m.
Common Mistakes to Avoid
- Mixing angle units: Do not plug degrees into s = rθ unless you convert to radians.
- Using diameter instead of radius: Radius is half of diameter.
- Negative values: For geometry length, use positive radius and non-negative angle.
- Forgetting circle context: Arc length is always part of a circle or circular path.
Where Arc Length Is Used in Real Life
- Road and railway curve design
- Gear and pulley systems
- CNC machining and manufacturing
- Robot arm motion paths
- Wheel rotation and travel distance calculations
- Architecture features like domes and arches
Quick Reference
Useful conversions
- Radians = Degrees × π / 180
- Degrees = Radians × 180 / π
- Circumference = 2πr
- Full circle = 360° = 2π radians
Final Thoughts
A reliable arc length calculator saves time and helps avoid unit errors. Whether you are solving homework problems or planning curved design dimensions, the key is simple: use the correct formula and keep angle units consistent. Enter your values above and calculate instantly.