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Degrees to Radians Converter: Convert Degrees to Radians

Convert angles from degrees (°) into radians (rad) using high-precision pi arithmetic.

Quick Answer:To convert degrees to radians, multiply the degree value by π and divide by 180. Formula: Radians = Degrees × π / 180.

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How to Use the Degrees to Radians Converter (rad = deg × π / 180)

1Enter the angle in degrees (°) into the input field.
2Select your preferred decimal precision (up to 8 decimal places).
3Read the converted radian (rad) value calculated with high-precision π.
4Inspect the step-by-step mathematical multiplication or copy the result.

Formula & How It Works

Trigonometric Radians Formula

Radians (rad) = Degrees (°) × (π ÷ 180)

Direct linear conversion derived from 360° = 2π radians. Source: ISO 80000-2 Mathematical Signs and Symbols.

Worked Examples

Converting a 90-Degree Right Angle

Input: 90°

Explanation: 90 × π / 180 = π / 2 = 1.570796... rad.

Result: 1.570796 rad (π/2)

Converting a 45-Degree Diagonal Angle

Input: 45°

Explanation: 45 × π / 180 = π / 4 = 0.785398... rad.

Result: 0.785398 rad (π/4)

Full 360-Degree Turn

Input: 360°

Explanation: 360 × π / 180 = 2π = 6.283185... rad.

Result: 6.283185 rad (2π)

Frequently Asked Questions

How do you convert degrees to radians?▼

Multiply the degree measurement by π and divide by 180. Radians = Degrees × π / 180.

What is 180 degrees in radians?▼

180 degrees is exactly π radians (approximately 3.14159265 rad).

What is 90 degrees in radians?▼

90 degrees is exactly π/2 radians (approximately 1.570796 rad).

What is 45 degrees in radians?▼

45 degrees is exactly π/4 radians (approximately 0.785398 rad).

Why do programming languages use radians for sin, cos, and tan?▼

Standard computer math libraries implement trigonometric Taylor series expansions, which are strictly valid only when input arguments are measured in radians.

Can I convert negative degrees?▼

Yes, negative degrees (like -90°) convert proportionally to negative radians (-1.5708 rad).

Quick Reference & Conversion Table

Degrees (°)	Exact Fraction of π	Radian Value	Geometric Role
0°	0	0.000000 rad	Zero orientation
30°	π/6	0.523599 rad	Hexagonal symmetry
45°	π/4	0.785398 rad	Octagonal symmetry
60°	π/3	1.047198 rad	Equilateral triangle
90°	π/2	1.570796 rad	Orthogonal perpendicular
180°	π	3.141593 rad	Reflection / Inversion
270°	3π/2	4.712389 rad	Three-quarter turn
360°	2π	6.283185 rad	Complete revolution

⚠️ Common Pitfalls to Avoid

•Multiplying by 180 / π instead of π / 180 (confusing degrees to radians with radians to degrees).
•Passing degree angles directly into programming language trig functions like Math.cos(45) without converting to radians first.
•Forgetting that negative degree angles (counterclockwise vs clockwise) yield negative radians.

💡 Practical Real-World Uses

•Preparing user angle inputs for coding algorithms in Three.js, WebGL, and Unity.
•Calculating pendulum oscillations, projectile trajectories, and celestial mechanics.
•Calibrating rotary encoders and CNC lathe cutting tool angles.

Last reviewed & updated: 2026-11-07

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