Radian Converter Formula

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

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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

DegreesRadiansPi Form 30°0.5236pi/6 45°0.7854pi/4 60°1.0472pi/3 90°1.5708pi/2 180°3.1416pi 360°6.28322pi

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

Frequently Asked Questions

What is a radian?

A radian is the angle subtended at the center of a circle by an arc equal in length to the radius. There are 2pi radians in a full circle.

What are gradians?

Gradians divide a right angle into 100 parts, so a full circle is 400 gradians. They are used in some surveying and engineering contexts.

Why is pi/4 radians equal to 45°?

A full circle is 360° = 2pi radians. So 45° = 45/360 × 2pi = pi/4 radians.

Learn More

Guide

Trigonometry Basics - Complete Guide

Learn the fundamentals of trigonometry including sine, cosine, tangent, the unit circle, identities, and the laws of sines and cosines with practical examples.

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