Bidirectional Degrees & Radians Converter | Angle Tool

How it Works & Assumptions

This tool uses standard trigonometric formulas to convert your input instantly. We assume all angles are in standard position (starting from the positive x-axis and rotating counter-clockwise). This ensures we can accurately determine the quadrant (I, II, III, or IV) for any given angle.

The Core Formulas

Converting between these two units is straightforward once you understand the relationship: 180° equals π radians.

• To Radians: Multiply your Degree value by π / 180.
• To Degrees: Multiply your Radian value by 180 / π.
• Exact Fractions: To get the "math class" answer (like 3π/2), we do not multiply by the approximate value of Pi (3.14...). Instead, we treat Pi as a symbol, find the fraction of the degrees over 180, and simplify it by finding the Greatest Common Divisor (GCD).

Quick Conversion Reference

Why Convert Between Degrees and Radians?

• Programming & Game Dev: Most math libraries (like JavaScript's Math.sin()) exclusively accept radians. If you feed them degrees, your game physics will break.
• Engineering: Torque, angular velocity, and rotational motion calculations rely on radians to keep formulas clean (avoiding the constant need for π/180 factors).
• Astronomy: Precise measurements of angular distance in the sky often require conversion between these units.

Frequently Asked Questions