Angle Converter

Angle unit conversions:

• 1 full rotation = 360 degrees = 2π radians = 400 gradians = 1 turn
• 1 degree = π/180 radians = 10/9 gradians = 1/360 turns
• 1 radian = 180/π degrees ≈ 57.2958° = 200/π gradians
• 1 gradian = 9/10 degrees = π/200 radians = 1/400 turns

Common angles:

• 90° = π/2 rad = 100 grad = 0.25 turns (right angle)
• 180° = π rad = 200 grad = 0.5 turns (straight angle)
• 360° = 2π rad = 400 grad = 1 turn (full rotation)
• 45° = π/4 rad = 50 grad = 0.125 turns
• 60° = π/3 rad = 66.667 grad = 0.1667 turns

Gradians (also called gon or grade) are used primarily in surveying and some European countries.

Degrees are the everyday unit, a full turn split into 360, a number the Babylonians chose because it divides so cleanly. Radians are the mathematician’s unit, and they aren’t arbitrary: one radian is the angle at which the arc length equals the radius. That definition is what makes calculus and physics formulas come out clean, which is why those fields assume radians rather than degrees. The most common real-world snag isn’t conversion at all, it’s calculator mode. A scientific calculator set to degrees gives a completely wrong answer for the sine or cosine of a value you meant in radians, and the reverse. If a trig result ever looks absurd, check the mode before anything else.