Central Angle Calculator for Arc Length

This calculator helps you find the central angle of a circle given the arc length and the radius. It's useful in geometry, engineering, and design applications.

Input Parameters

Calculation Results

Calculation Formula

Central Angle (θ) = (Arc Length / Radius) * (180/π)

Where:
θ = Central Angle in degrees
s = Arc Length
r = Radius
π = 3.141592653589793

Central Angle Calculator for Arc Length Calculator Usage Guide

Learn how to use the Central Angle Calculator for Arc Length calculator and its working principles

How to Use the Calculator

  1. Enter the arc length (s) of the circle in the first input field.
  2. Enter the radius (r) of the circle in the second input field.
  3. Click the "Calculate" button to compute the central angle.
  4. The result will be displayed in the "Central Angle (θ)" field.

Understanding the Formula

The central angle (θ) is calculated using the formula:

θ = (s / r) * (180/π)

Where:

  • s = Arc Length
  • r = Radius
  • π = Mathematical constant approximately equal to 3.14159

Example

If the arc length of a circle is 10 units and the radius is 5 units, the central angle would be:

θ = (10 / 5) * (180/π) ≈ 114.59 degrees

Applications

This calculator is useful in various fields including:

  • Architecture and engineering for designing circular structures
  • Navigation and astronomy for calculating celestial movements
  • Manufacturing for creating circular components
  • Art and design for creating circular patterns and shapes