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Arc Length Calculator

Calculate the arc length of a circle sector using radius and angle. Visual geometry tool with dynamic SVG rendering.

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Total Usage 3 times
Category Geometry & Planimetry
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About

This utility computes the length of an arc segment given the circle's dimensions. Precise arc length calculation is essential in mechanical engineering, architectural bending, and road layout design. Errors here result in material waste or structural misfit. The calculator accepts central angles in both degrees and radians, ensuring compatibility with various mathematical standards. It dynamically visualizes the resulting sector, aiding in the verification of parameters before application.

arc length sector calculator geometry circle math radians

Formulas

The core relationship depends on the ratio of the angle to a full circle.

L = θ360° × 2πr

When working with radians, the definition simplifies significantly because one radian creates an arc equal to the radius.

L = r × θ

Reference Data

Angle UnitFormulaTypical Use Case
Degrees (°)L = 2πr × (θ/360)General construction, Drafting
Radians (rad)L = rθCalculus, Physics, Higher Math
Gradians (grad)L = 2πr × (θ/400)Surveying (Europe), Mining
Minutes (')L = 2πr × (θ/21600)Navigation, Astronomy

Frequently Asked Questions

Yes. If you have the diameter, simply divide it by 2 to get the radius before inputting, or use the tool's diameter toggle if available.
They should be identical if the angle represents the same sector. Ensure you select the correct input mode. 180 degrees equals PI radians (approx 3.14159).
Yes, if the angle is greater than 360 degrees (or 2 PI radians), the arc wraps around the circle more than once. This represents a spiral or multi-turn coil.