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Trigonometry & Radians • Lesson 25 ⏱ 5 min read 📅 Updated Nov 2026

Degrees vs Radians: The Complete Conversion Guide and Formula

Understand why radians are the natural unit of angle measurement in calculus and science, and master converting between degrees and radians.

Core Formula

A radian measures angle using the circle’s own radius. Because Circumference = 2πr, a full 360° rotation equals exactly 2π radians.

Conversion Bridge

Radians = Degrees × (π180°)
Degrees = Radians × (180°π)
0° = 0 rad 45° = π/4 90° = π/2 rad 135° = 3π/4 180° = π rad Degrees → Radians: rad = deg × (π / 180) Radians → Degrees: deg = rad × (180 / π)
Degrees to Radians Conversion: A Straight Angle (180°) Equals Exactly π Radians (≈ 3.14159 rad)

Common Angle Benchmarks

DegreesRadians ExactRadians DecimalVisual Position
0°00.000 radEast (3 o’clock)
45°π/40.785 radNorth-East
90°π/21.571 radNorth (12 o’clock)
180°π3.142 radWest (9 o’clock)
270°3π/24.712 radSouth (6 o’clock)
360°2π6.283 radFull Rotation
Try It Yourself

Practice with Our Interactive Degrees to Radians Calculator

Check your calculations or explore full step-by-step solutions instantly.

Open Degrees to Radians Calculator →
Solved Step-by-Step Examples:180° to Radians (π)Radians Calculator
Your Turn!

Check Your Understanding (3 Quick Questions)

Score: 0 / 3

Question 1: How many radians are in a full 360° circle?

Question 2: Convert 90° into radians:

Question 3: To convert radians to degrees, multiply by: