Convert A Number to Degrees Calculator

Converting numbers to degrees is a fundamental skill in mathematics, engineering, and science. This calculator provides a simple way to convert between different angle units, including radians, gradians, and other common measurements.

How to Convert a Number to Degrees

The process of converting a number to degrees depends on the original unit of measurement. Here are the most common conversion formulas:

Radians to Degrees

Degrees = Radians × (180/π)

Example: 1 radian = 1 × (180/3.1416) ≈ 57.2958 degrees

Gradians to Degrees

Degrees = Gradians × (9/10)

Example: 100 gradians = 100 × (9/10) = 90 degrees

Turns to Degrees

Degrees = Turns × 360

Example: 0.5 turns = 0.5 × 360 = 180 degrees

To convert between these units, simply multiply the original value by the appropriate conversion factor. The calculator on this page handles these conversions automatically for you.

Common Angle Unit Conversions

Here's a quick reference table for common angle unit conversions:

From Unit	To Degrees	Example
Radians	Multiply by 180/π	π/2 radians = 90 degrees
Gradians	Multiply by 9/10	100 gradians = 90 degrees
Turns	Multiply by 360	0.25 turns = 90 degrees
Minutes of Arc	Divide by 60	3600 minutes = 60 degrees
Seconds of Arc	Divide by 3600	129600 seconds = 36 degrees

This table provides a quick reference for converting between different angle units. The calculator on this page can handle all these conversions automatically.

Practical Examples

Here are some practical examples of converting numbers to degrees:

Example 1: Converting Radians to Degrees

Problem: Convert 2 radians to degrees.

Solution: 2 × (180/π) ≈ 114.5916 degrees

This conversion is useful in trigonometry and physics when working with circular functions.

Example 2: Converting Gradians to Degrees

Problem: Convert 50 gradians to degrees.

Solution: 50 × (9/10) = 45 degrees

This conversion is commonly used in surveying and navigation.

Example 3: Converting Turns to Degrees

Problem: Convert 0.75 turns to degrees.

Solution: 0.75 × 360 = 270 degrees

This conversion is useful when working with full rotations or circular measurements.

These examples demonstrate how to convert between different angle units in practical scenarios. The calculator on this page can handle all these conversions automatically for you.

FAQ

What is the difference between degrees, radians, and gradians?: Degrees, radians, and gradians are all units of angular measurement. Degrees are the most common in everyday use, radians are commonly used in calculus and physics, and gradians are used in some European countries for surveying and navigation.
How do I convert degrees to radians?: To convert degrees to radians, multiply the degree value by π/180. For example, 90 degrees = 90 × (π/180) = π/2 radians.
What is the difference between a turn and a degree?: A turn is a unit of angular measurement equal to 360 degrees. One turn represents a full rotation around a circle. For example, 0.5 turns = 180 degrees.
How accurate is this calculator?: This calculator uses standard mathematical formulas and provides results with up to 6 decimal places for precision. The formulas and assumptions are clearly displayed on the page for transparency.
Can I use this calculator for professional work?: Yes, this calculator can be used for professional work, but always verify critical calculations with a more specialized tool if needed. The formulas and assumptions are clearly displayed for your reference.