Convert Radians to Degrees - Fast & Accurate Radians ⇄ Degrees Conversion Tool

Need a fast and accurate way to convert radians to degrees or degrees to radians? Our Radians ⇄ Degrees Converter gives instant results with precise calculations. Enter your value and get quick, reliable answers anytime.

Why Users Love This Radians ⇄ Degrees Converter

• Exact in design: Based on the correct trigonometric formula for perfect results.
• Instant answers: Get accurate conversions in real-time as you type.
• Clear display: Shows both the exact and rounded values with adjustable decimal places.
• Two-way switch: Easily toggle between radians to degrees and degrees to radians. 
• Works anywhere: Fully mobile and desktop friendly for classroom, lab, or daily use.

How to Use Our Converter

1. Enter the value in radians or degrees.
2. Choose the conversion direction — Radians to Degrees or Degrees to Radians.
3. View your instant result.
4. Copy, share, or save the converted value.

Radians

The term radian (rad) measures angles using the length of the arc compared to the circle’s radius. It’s a standard unit in mathematics, trigonometry, and physics, especially when working with sine, cosine, and tangent functions.

Key Facts About Radians

• Exact value: 1 radian = 180/π degrees
• Relationship to other units: 2π radians = 360 degrees
• Common abbreviation: rad
• Notation tips: Often written without the symbol but always assumed to be radians in formulas.

Degrees

The term degree (°) represents a part of a full circle, where a full rotation equals 360°. Degrees are used in geometry, navigation, astronomy, and engineering for measuring angles or directions.

Key Facts About Degrees

• Exact value: 360° = 2π radians
• Relationship to other units: 1° = π/180 radians
• Common abbreviation: °
• Notation tips: Always include the degree symbol (°) after the numeric value.

Radians to Degrees Conversion Formula

Formula:

Degrees = Radians × (180 / π)

Radians to Degrees Conversion Examples

Example 1: 1 radian to degrees
Step 1: Formula = Degrees = Radians × (180 / π)
Step 2: Substitute = 1 × (180 / π)
Step 3: Multiply = 57.2958°

Example 2: π/2 radians to degrees
Step 1: Degrees = Radians × (180 / π)
Step 2: Substitute = (π/2) × (180 / π)
Step 3: Result = 90°

Example 3: π radians to degrees
Step 1: Degrees = Radians × (180 / π)
Step 2: Substitute = π × (180 / π)
Step 3: Result = 180°

Degrees to Radians Conversion Formula

Formula:

Radians = Degrees × (π / 180)

Degrees to Radians Conversion Examples

Example 1: 30° to radians
Step 1: Formula = Radians = Degrees × (π / 180)
Step 2: Substitute = 30 × (π / 180)
Step 3: Multiply = π/6 radians

Example 2: 90° to radians
Step 1: Radians = Degrees × (π / 180)
Step 2: Substitute = 90 × (π / 180)
Step 3: Result = π/2 radians

Example 3: 180° to radians
Step 1: Radians = Degrees × (π / 180)
Step 2: Substitute = 180 × (π / 180)
Step 3: Result = π radians

Applications of Radians and Degrees Conversions

• Trigonometry: Used for solving angles and sides in triangles.
• Physics: Converts angular motion, torque, and wave rotations.
• Engineering: Important for design calculations and mechanics.
• Astronomy: Helps measure the positions and rotations of celestial bodies.

Quick Reference Table for Radians ⇄ Degrees Conversion

Use our Radians ⇄ Degrees Converter at Digital Calculator for fast, accurate, and reliable conversions in math, physics, and engineering. Whether you’re a student, teacher, or professional, this free tool simplifies your work instantly.