Degree & Radian Conversion

How to switch between DEG and RAD modes

Overview

In scientific calculations, angles can be expressed in two different units:

  • Degrees (DEG): Circle divided into 360 equal parts, each part is 1 degree
  • Radians (RAD): Angle subtended when arc length equals radius is 1 radian

The calculator supports switching between the two modes for different calculation needs.

Conversion Formula

180° = π radians
1° = π/180 radians ≈ 0.01745 radians
1 radian = 180/π degrees ≈ 57.2958°
Common Degree-Radian Conversion Table
Degrees Radians
0°0
30°π/6
45°π/4
60°π/3
90°π/2
180°π
270°3π/2
360°2π

How to Switch Modes

In the calculator's mode toggle area, click DEG or RAD button to switch angle mode.

  • DEG: Degree mode, input values are treated as degrees
  • RAD: Radian mode, input values are treated as radians

Examples

Example 1: DEG mode - sin(30)
Mode: DEG
Input: sin(30)
Result: 0.5
30 means 30°
Example 2: RAD mode - sin(π/6)
Mode: RAD
Input: sin(pi/6)
Result: 0.5
π/6 radians equals 30°
Example 3: Manual conversion
Input: 45 * pi / 180
Result: 0.785398... (π/4 radians)
Convert 45° to radians

When to Use Each Mode

Use Degree Mode (DEG) for:

  • Everyday and engineering applications
  • Geography and navigation calculations
  • Elementary math problems

Use Radian Mode (RAD) for:

  • Advanced mathematics and calculus
  • Physics formulas
  • Scientific computing and programming
  • Derivatives and integrals of trigonometric functions

Important Notes

  1. After switching modes, trigonometric function results update immediately
  2. Most programming languages use radians by default
  3. Inverse trigonometric function return values also change based on current mode
  4. Always check the current mode to avoid calculation errors

Related Topics

Trigonometric Functions Inverse Trig Functions Math Constants