Angle calculator
A radian is the angle subtended by an arc equal in length to the radius, which makes 2π radians a full turn. Degrees are an arbitrary 360 inherited from Babylonian astronomy; radians are not arbitrary at all. That is why calculus is written in radians — the derivative of sin x is cos x only if x is in radians, and picks up an awkward factor of π/180 otherwise.
180 degrees is π radians, 200 gradians and half a turn. To convert degrees to radians multiply by π/180; to go back multiply by 180/π. A 45 degree angle is 0.7854 radians.
How to convert angles
Gradians are the unit almost nobody uses and they exist for a reason: a right angle is exactly 100 gradians and a full turn 400, which makes surveying arithmetic decimal throughout. They survive in some European surveying equipment and in a key on most scientific calculators that is pressed only by accident. Arcminutes and arcseconds — sixtieths and three-thousand-six-hundredths of a degree — remain genuinely standard in astronomy and navigation.
Questions
Multiply by π and divide by 180. Ninety degrees is π/2, about 1.5708.