Convert angles between degrees, radians, gradians and turns for maths, code and drawings.
Calculations happen locally. We do not send your values to our server.
A full turn is 360 degrees or about 6.28318531 radians, so 180° is about 3.14159265 rad and 1 radian is about 57.29577951°. In other units, 90° is exactly 100 gradians and 45° is 0.125 turn.
Every angle is normalised to radians, since a full turn is 2π radians, 360 degrees or 400 gradians. Gradians divide a right angle into 100 parts, and a turn is one complete revolution, so the conversions are exact ratios rather than approximations.
The tool works in decimal degrees. Map coordinates often use arc minutes and arc seconds, where a degree holds 60 minutes and 3,600 seconds, so convert those first: 30.5° is the same as 30°30′. Negative angles and values beyond one turn are accepted and use the same factors.
A full turn is 360 degrees or 2π radians, so 180° is π, about 3.14159265 rad, and 360° is about 6.28318531 rad. One radian, the angle whose arc equals the radius, is about 57.29577951°. Most programming languages and scientific formulas expect radians, so a sine or cosine function given 30 expects 30 radians rather than 30 degrees unless the calculator is set to degree mode. Convert degrees to radians before using those functions in code or spreadsheets.
Gradians, also called gons, divide a right angle into 100 parts and a full circle into 400, so 90° is exactly 100 gradians and 100 gradians is 90°. They appear in some surveying instruments and on the grad setting of calculators, which can cause confusing trigonometry answers when selected by mistake. A turn is one complete revolution; 45° is 0.125 turn. Turns are convenient for rotation in animation and mechanical drawings, where a quarter turn is easier to read than 90°.
Degrees can be divided into 60 arc minutes and each minute into 60 arc seconds, as in map coordinates: 30.5° is 30°30′. This converter uses decimal degrees, so convert minutes and seconds by dividing by 60 and 3,600 before entering them. A slope percentage is not an angle unit: a 100% grade rises as much as it runs and equals 45°, while a 10% road grade is only about 5.71°. Use the arctangent of the grade to find its angle.
| Input | Result |
|---|---|
180 degree → radian | 3.14159265 |
360 degree → radian | 6.28318531 |
1 radian → degree | 57.29577951 |
90 degree → gradian | 100 |
45 degree → turn | 0.125 |
100 gradian → degree | 90 |
In most programming languages and scientific formulas. A sine or cosine function given 30 treats it as 30 radians, not 30 degrees, unless a calculator is explicitly in degree mode. Convert degrees to radians before using those functions in code or spreadsheets, and remember that 180° is about 3.14159265 rad.
A unit that divides a right angle into 100 parts and a full circle into 400, also called a gon. So 90° is exactly 100 gradians and 100 gradians is 90°. Gradians appear on surveying instruments and on the grad setting of pocket calculators, which is a common cause of confusing trigonometry answers when selected by mistake.
No. A 100% grade rises as much as it runs, which equals 45°, while a 10% road grade is only about 5.71°. Take the arctangent of the grade to find the angle. Turns are a different matter: they are true angle units, and 45° is 0.125 turn, which is often easier to read on rotation and animation settings.