Cyber Security • RF • Conversions

Degrees to Radians Conversion

to
Degrees
°
Result
Calculation steps

About Degrees to Radians

This page converts degrees to radians instantly, with a clear formula, worked examples, and a quick reference table.

Angle conversions are common in math, engineering, navigation, surveying, CAD, and astronomy—different fields prefer different angle units.

Quick context

Radians (rad) are the standard angle unit in many math, physics, and engineering formulas. They connect angles directly to circle geometry (arc length ÷ radius), which is why calculus and trigonometry often assume radians.

People convert degrees to radians because many scientific formulas and programming libraries expect angles in radians.

Formula: Degrees to Radians

Radians = Degrees × 0.01745329252

Worked examples

Convert 1 Degrees to Radians
  1. Start with: 1 Degrees.
  2. Use: Radians = Degrees × 0.01745329252.
  3. Compute: 1 × 0.01745329252 = 0.01745329252.
  4. Answer: 0.01745329252 Radians.
Convert 30 Degrees to Radians
  1. Start with: 30 Degrees.
  2. Use: Radians = Degrees × 0.01745329252.
  3. Compute: 30 × 0.01745329252 = 0.523598775598.
  4. Answer: 0.523598775598 Radians.
Convert 45 Degrees to Radians
  1. Start with: 45 Degrees.
  2. Use: Radians = Degrees × 0.01745329252.
  3. Compute: 45 × 0.01745329252 = 0.785398163397.
  4. Answer: 0.785398163397 Radians.
Convert 90 Degrees to Radians
  1. Start with: 90 Degrees.
  2. Use: Radians = Degrees × 0.01745329252.
  3. Compute: 90 × 0.01745329252 = 1.570796326795.
  4. Answer: 1.570796326795 Radians.

Conversion table

DegreesRadians
00
150.261799387799
300.523598775598
450.785398163397
601.047197551197
901.570796326795
1803.14159265359
3606.28318530718

FAQs

What is the formula to convert degrees to radians?
Multiply the value in degrees by 0.01745329252 to get radians. In short: Radians = Degrees × 0.01745329252.
Why are radians used in math and physics?
Many formulas in calculus, trigonometry, and physics assume radians because radians link angles to circle geometry (arc length ÷ radius). This removes extra constants and makes formulas cleaner.
What are quick reference values for degrees to radians?
Common ones are 30° = π/6, 45° = π/4, 90° = π/2, 180° = π, 360° = 2π.
Is radian an SI unit?
Yes. The radian (rad) is the standard SI-based unit used in science and engineering for plane angles.