How to Use the Coterminal Angle Calculator

Enter an angle in degrees. The calculator returns its angle normalized to 0–360°, plus one positive and one negative coterminal angle.

coterminal angle = angle ± (360° × n),  for any integer n

Two angles are coterminal when they end up pointing the same direction after all the spinning is done — 30°, 390°, and −330° all land on the exact same ray, since each just adds or removes one full 360° turn. That matters anywhere an angle gets generated by repeated rotation (gears, orbits, compass bearings): the number of turns can pile up indefinitely, but the direction it actually points only ever depends on that number reduced to a single trip around the circle.