Arc Length Calculator

Simple & Fast Calculations

Use this arc length calculator to find arc length, radius, or central angle.

Enter any two values, then get the third in seconds.

The page shows the formula and a clear worked solution.

A simple diagram highlights each part of the circle.

How It Works

The math uses s = r × θ where θ is in radians.

With degrees, the tool converts angle to radians using θ = degrees × π/180.

You provide two inputs. The calculator finds the missing value.

What each field means.

• Radius r: Use the same unit as arc length. Enter a positive number.
• Central angle θ in degrees: Type the angle in degrees. Decimals work fine.
• Arc length s: Use the same unit as radius. Enter a positive length.

How to read the output.

• If you enter r and θ, the result is s.
• If you enter r and s, the result is θ in degrees.
• If you enter θ and s, the result is r.
• The solution shows each step, including the radians conversion and the final value.
• The main result rounds to two decimals. The radians value shows four decimals.

Notes and limits.

• Enter exactly two values for a valid result.
• Use consistent units for radius and arc length.
• The angle input accepts degrees only.
• Large angles compute correctly. The diagram displays up to 360 degrees.

How to Use This Tool

1. Decide which two values you know.
2. Enter the radius if you have it.
3. Enter the central angle in degrees if you have it.
4. Or enter the arc length if you have it.
5. Click Calculate to solve for the missing value.
6. Review the step by step solution under the inputs.
7. Click Clear All to start a new calculation.

Why Use the Arc Length Calculator?

This tool saves time and cuts errors on circle arc problems.

It shows the formula and the steps.

It gives a clean result you can trust.

The diagram adds context for students and teachers.

Makers gain quick visual checks.

Use it for homework and design checks.

It works for quick field math.

Real Benefits for Everyday Users

Here are common cases where this arc length calculator helps.

• Geometry work: Find arc length from a known radius and angle.
• Computer aided design: Confirm arc lengths in sketches and drawings.
• Woodworking or metalwork: Set jigs and cut smooth arcs with the right length.
• Piping and ducts: Estimate bend lengths for elbows and sweeps.
• Athletics and fields: Measure track sectors or circular fence runs.
• Robotics and computer numerical control machines: Convert turn angles to path length.

Quick examples make the method clear.

• Given r = 10 and θ = 90 degrees: s = 10 × π/2 gives about 15.71.
• Given r = 10 and s = 31.42: θ = s ÷ r gives 3.1416 radians which is 180 degrees.
• Given θ = 45 degrees and s = 7.85: r = s ÷ 0.7854 gives about 10.

Keep units consistent across inputs and outputs for clean results.