Arc Calculator
Compute arc length, sector area, and chord length from radius and angle.
Arc measurements
Use the same length unit for radius and the resulting arc length.
Angles may exceed 360° (2π radians); the calculator will still compute proportional arc values.
Table of Contents
How to Use
- Enter the radius of the circle using any length unit.
- Provide the central angle and choose degrees or radians.
- Click Calculate to convert the angle and compute arc metrics.
- Review arc length, sector area, chord length, and the detailed steps.
Arc Length Basics
Arc length measures the distance along a circle between two points. It is proportional to the radius and the central angle measured in radians.
Formula: s = r × θ, where θ must be in radians. Convert degrees to radians by multiplying by π/180.
Sector Area and Perimeter
The area of a circular sector is A = ½ r² θ. The total perimeter of the sector equals the arc length plus two radii.
Half the angle gives you the triangle needed for chord length: c = 2r sin(θ/2).
Where These Calculations Matter
- Engineering: belt drives, pulley design, and gear tooth spacing.
- Architecture: designing arches, domes, and curved facades.
- Manufacturing: sheet metal bending and laser cutting paths.
- Navigation: mapping great-circle distances and course changes.
- Education: teaching relationships between radians and degrees.
Frequently Asked Questions
- Can I use different units for radius and arc length?
- Keep the same unit for radius and the arc length result will share that unit. If you need a different unit, convert after calculating.
- What happens if the angle is larger than 360°?
- Angles over 360° represent multiple turns. The calculator scales the arc metrics proportionally—for example, 720° gives an arc length twice the circumference.
- Does the calculator support negative angles?
- Angles must be positive. If you have a negative angle, convert it to its positive equivalent before entering it.