Radian Converter Formula

Understand the math behind the radian converter. Each variable explained with a worked example.

Use the Radian Converter

Formulas Used

Radians

radians = deg * pi / 180

Pi Fraction

pi_fraction = deg / 180

Gradians

gradians = deg * 10 / 9

Variables

VariableDescriptionDefault
degDegrees(deg)45

How It Works

Radian Conversion

Formulas

Radians = Degrees × pi/180

Degrees = Radians × 180/pi

Common Conversions

| Degrees | Radians | Pi Form | |---------|---------|--------| | 30° | 0.5236 | pi/6 | | 45° | 0.7854 | pi/4 | | 60° | 1.0472 | pi/3 | | 90° | 1.5708 | pi/2 | | 180° | 3.1416 | pi | | 360° | 6.2832 | 2pi |

Worked Example

Convert 45° to radians.

deg = 45
  1. 01Radians = 45 × pi/180 = pi/4
  2. 02= 0.7854 radians
  3. 03Gradians = 45 × 10/9 = 50 grad

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Open Radian Converter