Angle Converter

Multiply degrees by pi/180. For example: 90 degrees = 90 x (pi/180) = pi/2 radians = 1.5708 rad. Conversely, multiply radians by 180/pi to get degrees. Key values: 180 degrees = pi rad, 360 degrees = 2*pi rad, 45 degrees = pi/4 rad. The converter handles any value instantly.

Gradians (also called grads or gon) divide a right angle into 100 parts instead of 90 degrees. A full circle is 400 gradians. They are used primarily in surveying and some European engineering contexts. 1 gradian = 0.9 degrees = pi/200 radians.

An arcminute is 1/60 of a degree. An arcsecond is 1/60 of an arcminute (1/3600 of a degree). These tiny units are used in astronomy, navigation, and GPS coordinates. For example, GPS coordinates often include degrees, minutes, and seconds: 40 degrees 26 minutes 46 seconds N.

Radians are the natural unit for angles in mathematics. Calculus formulas (derivatives and integrals of trig functions) only work cleanly in radians. The formula for arc length (s = r*theta) requires theta in radians. Programming languages and scientific calculators default to radians for these reasons.

A turn (also called revolution or cycle) is one complete rotation: 360 degrees = 2*pi radians = 400 gradians = 1 turn. Half a turn is 180 degrees. Quarter turn is 90 degrees. Turns are intuitive for describing rotations and are used in some engineering and physics contexts.