Calculate the 90° complement, 180° supplement, and acute reference angle of an angle in degrees.
| Complement (90-θ) | – |
| Supplement (180-θ) | – |
| Reference (0-90) | – |
Use this calculator to relate an angle in degrees to its complement, its supplement, and its reference angle. Two angles are complementary if they add to 90° and supplementary if they add to 180°. The reference angle is the acute (or right) angle that a direction in standard position makes with the nearest x-axis, always between 0° and 90°.
The complement is 90° − θ and the supplement is 180° − θ, computed from the angle as entered; either result can be negative if θ is larger than 90° or 180°. The reference angle first reduces θ modulo 360° into [0°, 360°) and then folds that measure into [0°, 90°]. Coterminal angles differ from θ by a multiple of 360° and share the same reference angle.
Angle (°): Any real degree measure.
Complement (90−θ): 90° minus the entered angle.
Supplement (180−θ): 180° minus the entered angle.
Reference (0–90): Acute or right angle to the x-axis after reducing modulo 360°.
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