Angle in Degrees Calculator

An angle in degrees is a measure of rotation between two rays. Degrees are commonly used in geometry, navigation, and engineering. This calculator helps you convert between degrees and other angle units.

What is Angle in Degrees?

The degree is a unit of angle measurement in the International System of Units (SI). A full circle is 360 degrees, with each degree divided into 60 minutes and each minute into 60 seconds. Degrees are widely used in everyday applications, navigation, and scientific calculations.

Angles in degrees are used in various fields including:

Geometry and trigonometry
Navigation and surveying
Engineering and construction
Computer graphics and animation
Everyday measurements like compass bearings

How to Convert Degrees

Converting between degrees and other angle units is essential for many calculations. Here are the common conversions:

Degrees to Radians

Radians are the SI unit for angles. To convert degrees to radians, use the formula:

Radians = Degrees × (π/180)

For example, 90 degrees is equal to π/2 radians.

Degrees to Gradians

Gradians are another angle unit where a full circle is 400 gradians. The conversion formula is:

Gradians = Degrees × (400/360)

For example, 90 degrees is equal to 100 gradians.

Degrees to Turns

A turn is a unit where a full circle is 1 turn. The conversion formula is:

Turns = Degrees/360

For example, 180 degrees is equal to 0.5 turns.

Common Angle Conversions

Here's a table showing common angle conversions:

Degrees	Radians	Gradians	Turns
0°	0	0	0
45°	π/4	50	0.125
90°	π/2	100	0.25
180°	π	200	0.5
270°	3π/2	300	0.75
360°	2π	400	1

This table provides quick reference points for common angle measurements in different units.

Angle in Degrees Formula

The basic formula for converting between angle units is:

General Angle Conversion Formula

To convert between any two angle units, use the following formula:

New Unit = Original Value × (Conversion Factor)

The conversion factors are:

Degrees to Radians: π/180
Degrees to Gradians: 400/360
Degrees to Turns: 1/360

For example, to convert 120 degrees to radians:

120° × (π/180) = 2π/3 radians

FAQ

What is the difference between degrees and radians?

Degrees are based on the division of a circle into 360 equal parts, while radians are based on the radius of a circle. A full circle is 2π radians, which is approximately 360 degrees. Radians are the standard unit in mathematics and physics, while degrees are more common in everyday applications.

How do I convert degrees to gradians?

To convert degrees to gradians, multiply the degree value by 1.111111 (400/360). For example, 90 degrees is 100 gradians (90 × 1.111111).

What is a full circle in degrees?

A full circle is 360 degrees. This is based on the ancient Babylonian division of a circle into 360 parts, which was later adopted by the Greeks and Romans.

Can I use this calculator for navigation purposes?

Yes, this calculator is useful for navigation purposes, including converting compass bearings and other angle measurements. However, always verify your calculations with other tools for critical navigation tasks.