Degrees
A full circle contains 360 degrees. Degrees are widely used in geometry, navigation, construction, design and everyday angle measurements.
Understanding angle measurements
What Is an Angle Unit?
An angle unit measures rotation between two rays, lines or directions. Degrees and radians are the most common units, while other systems are used in surveying, navigation, astronomy and engineering.
Radians
A full circle contains 2π radians. Radians are the standard angle unit used in advanced mathematics, trigonometry, calculus and physics.
Simple process
How to Use the Angle Converter
The result updates automatically whenever you enter a value or change either angle unit.
Enter the angle
Type the angle value you want to convert into the first input field.
Select the original unit
Choose degrees, radians, gradians, turns, arcminutes or another supported unit.
Choose the result unit
Select the destination unit to view the converted value and equivalent measurements instantly.
Conversion formulas
Common Angle Conversion Formulas
These formulas can be used to check common angle conversions manually.
Degrees to Radians
Radians = Degrees × π ÷ 180
Example: 180 degrees equals π radians.
Radians to Degrees
Degrees = Radians × 180 ÷ π
Example: π/2 radians equals 90 degrees.
Degrees to Gradians
Gradians = Degrees × 10 ÷ 9
Example: 90 degrees equals 100 gradians.
Degrees to Turns
Turns = Degrees ÷ 360
Example: 90 degrees equals 0.25 turns.
Common values
Common Angle Conversion Table
These values show frequently used relationships between degrees, radians, gradians and turns.
| Degrees | Radians | Gradians | Turns |
|---|---|---|---|
| 0° | 0 | 0 gon | 0 |
| 30° | π/6 | 33.3333 gon | 0.0833333 |
| 45° | π/4 | 50 gon | 0.125 |
| 60° | π/3 | 66.6667 gon | 0.166667 |
| 90° | π/2 | 100 gon | 0.25 |
| 180° | π | 200 gon | 0.5 |
| 270° | 3π/2 | 300 gon | 0.75 |
| 360° | 2π | 400 gon | 1 |
Smaller angle units
Arcminutes, Arcseconds and Milliradians
Smaller angle units are useful where greater precision is required.
Arcminutes and Arcseconds
One degree contains 60 arcminutes, and one arcminute contains 60 arcseconds. These units are commonly used in astronomy, navigation and mapping.
Milliradians and Mils
A milliradian is one-thousandth of a radian. NATO angular mils divide a complete circle into 6,400 equal parts.
Helpful answers
Frequently Asked Questions
Multiply the degree value by π and divide by 180. For example, 180 degrees multiplied by π/180 equals π radians.
One radian is approximately equal to 57.2957795 degrees.
One full turn equals 360 degrees, 2π radians or 400 gradians.
A gradian divides a right angle into 100 equal parts. One full circle contains 400 gradians.
An arcminute is one-sixtieth of one degree. One degree contains 60 arcminutes.
An arcsecond is one-sixtieth of an arcminute or one three-thousand-six-hundredth of a degree.
Yes. Negative angles are supported. The live visualizer normalizes the direction into the range from 0 to less than 360 degrees.
Precision note:
Results may be rounded for display. The converter keeps
higher internal precision when calculating between angle
units.