Arc Length Calculator

The length of a portion of a circle's circumference.

How the Math Works

The Arc Length Calculator uses the fundamental formula arc = (angle ÷ 360) × 2πr to determine the distance along a circular curve. This relationship works because a full circle contains 360 degrees and has a total circumference of 2πr. By taking the ratio of your central angle to the full circle, you're calculating what fraction of the complete circumference your arc represents. Multiplying this fraction by the total circumference gives you the precise arc length, making it simple to find partial circle distances without complex trigonometry.

Practical Applications

To use this calculator practically, simply input the radius of your circle and the central angle in degrees. For example, if you need to find the length of a circular pipe segment with a radius of 5 feet and a central angle of 72 degrees, plug these values into the calculator. The tool will automatically handle the multiplication and division, giving you the exact arc length. This is invaluable for construction projects, engineering designs, and manufacturing processes where precise curved measurements are essential for fitting components together correctly.

Day-to-Day Use

Arc length calculations appear in everyday situations more than you might realize. When installing a fence around a circular garden, determining the amount of curved wallpaper trim needed for a round room, or calculating the shortest path for a walking trail that follows a curved path, this calculator provides the exact measurements you need. Even when driving and estimating distances around curved roads or when crafting circular decorations at home, understanding arc length helps you make accurate material estimates and plan efficiently without wasting resources or running short on supplies.

Worked example

r 5, 90° → 7.85.

FAQ