Reference Angle Calculator

Enter any angle to calculate its reference angle and quadrant.

How to Use the Reference Angle Calculator

Enter any angle in degrees — negative values and values past 360° both work. The calculator normalizes it to 0–360°, reports which quadrant it falls in, and returns the reference angle.

Quadrant I (0–90°):    reference angle = angle
Quadrant II (90–180°):  reference angle = 180° − angle
Quadrant III (180–270°): reference angle = angle − 180°
Quadrant IV (270–360°): reference angle = 360° − angle

A reference angle is always the acute angle between the terminal side and the x-axis — never the y-axis, and never more than 90° — which is what makes it useful: sin, cos, and tan of any angle, however large or negative, always match the reference angle's values up to a sign determined by the quadrant. Look up one acute angle's trig ratios and every coterminal, reflected, or rotated version of it is already solved.