Angle Converter
Convert an angle between degrees, radians, gradians and revolutions - handy for geometry, trigonometry and engineering drawings.
About the Angle Converter
This tool converts an angle between degrees, radians, gradians, arcminutes, arcseconds and full revolutions. These units come up in maths, trigonometry, surveying, navigation and engineering drawings, where the same angle is often expressed in whichever system fits the field.
How to use it
- Enter the angle you know into its field, for example 90 in the degrees field.
- Read the equivalent in radians, gradians or revolutions.
- Use arcminutes and arcseconds for fine angular measurements in astronomy or surveying.
The key relationships: a full circle is 360 degrees, which equals 2 pi radians, 400 gradians or 1 revolution. So 180 degrees is pi radians and 90 degrees is pi/2 radians. Radians are the natural unit for calculus and trigonometric functions in most programming languages, which is why this converter is handy when a function expects radians but your data is in degrees. One degree splits into 60 arcminutes and each arcminute into 60 arcseconds. Everything runs in your browser with no data uploaded.
Frequently asked questions
How do I convert degrees to radians?
Multiply degrees by pi/180 (about 0.01745). So 180 degrees equals pi radians (about 3.1416) and 90 degrees equals pi/2 radians.
How many radians are in a full circle?
A full circle is 2 pi radians, about 6.2832. That equals 360 degrees, 400 gradians or one revolution.
What is a gradian?
A gradian (or gon) divides a right angle into 100 parts, so a full circle is 400 gradians. It is used in some surveying and engineering contexts.
How many arcseconds are in a degree?
One degree contains 60 arcminutes, and each arcminute contains 60 arcseconds, so a degree is 3600 arcseconds. These fine units matter in astronomy and precision surveying.