How to use Angle Converter
- Enter the Value in the unit you have, for example 45.
- Choose Convert from, such as Degrees.
- Choose Convert to, such as Radians (rad).
- Set the Seconds precision used by the degrees, minutes and seconds row.
- The result, the decimal degree row and the DMS row update as you change the values.
Example: Angle Converter
Convert degrees to radians.
Options
- Seconds precision
- Sets the decimal places on the seconds in the degrees, minutes and seconds row. The seconds are rounded as a total, so a value just under a whole degree carries instead of printing 60 minutes or 60 seconds.
- Convert to
- Degrees, radians, gradians, turns, arcminutes and arcseconds each appear as their own unit. A full turn is 360 degrees and 400 gradians.
Supported inputs and limits
Where your input is processed
This tool processes your input in this browser. Your text and files are not uploaded to UseFreeTools. Check this tool's limits for anything it may save on your device.
Why pi is the only rounding in the angle factors
A turn, a gradian, an arcminute and an arcsecond are fixed fractions of a degree, so those factors are exact. The radian is different: it is the angle of an arc as long as its radius, which makes it 180 divided by pi degrees, and pi cannot be written exactly as a decimal. The tool holds pi to 50 decimal places and works at 60 significant digits, so a radian result is limited by that constant instead of by the arithmetic.
NIST Special Publication 811, Appendix B.8: degree, gon and revolution factors
Why the total is rounded before it is split
Converting decimal degrees to minutes and seconds means splitting a number into a whole part and a remainder twice. If each part were rounded on its own, a value a hair below a whole degree could print as 59 degrees and 60 minutes, or a whole minute could print as 59 seconds and 60 arcseconds. Rounding the total number of seconds first and then splitting removes that case, and the page states which precision was applied.
NIST Special Publication 811, Appendix B.8: minute and second of angle factors
Questions about Angle Converter
How many degrees is one radian?
A radian is 180 divided by pi degrees, about 57.29577951308232 degrees. Put the other way, a full turn is two pi radians.
Why does the tool show degrees, minutes and seconds as well?
Surveying, navigation and astronomy often use the degrees, minutes and seconds form while a calculator returns decimal degrees. The row is there so a decimal result does not have to be converted by hand, and it is the same reading whichever unit you chose.
Can the seconds show 60?
No. The total number of seconds is rounded once before it is split into degrees, minutes and seconds, so a value just under a whole degree becomes 60 degrees, 0 minutes and 0 seconds rather than a minute or a second of 60.
How many degrees is a gradian or a turn?
One turn is exactly 360 degrees, and one gradian is exactly 0.9 degrees, which makes a full turn 400 gradians. Both convert exactly because they do not involve pi.
Is this the same as a compass bearing?
No. This tool converts plane angles. A compass bearing also depends on the reference direction and on magnetic variation, which are outside a unit conversion.