Angle Converter
How it works
Degrees is the basis every value passes through: radians and gradians are both most naturally defined in terms of it (360° = 2π radians = 400 gradians), so converting between the other two goes via degrees rather than carrying π through a gradians-to-radians formula directly.
Unlike a length or a percentage, an angle has no natural floor or ceiling, so nothing here rejects a negative value or one past 360° — both describe a real orientation, just not the smallest way of writing it.
Frequently asked questions
What are gradians, and where are they used?
A gradian (also called a "gon") divides a right angle into 100 equal parts instead of 90, so a full turn is 400 gradians rather than 360 degrees. The appeal is decimal-friendliness — a quarter turn is a round 100 gon — and it shows up mainly in surveying and on some scientific calculators and software, rather than in everyday use.
Why does this tool accept negative angles or values over 360 degrees?
Because both describe something real. A rotation of -45° is a turn the other way, and 720° is two full turns rather than one — neither is a mistake to correct. This converter treats degrees the way a rotation actually works rather than wrapping every value into a 0-360° range.
What are the exact conversion constants?
A half turn is 180 degrees, exactly π radians, and exactly 200 gradians — worth keeping in mind to sanity-check any result by hand. From there, one degree is π/180 radians, and one degree is 400/360 (or 10/9) gradians.