Complementary Angles Calculator
Enter an angle between 0° and 90° to instantly find its complementary angle, supplementary angle, and the trig cofunction values that link the two angles in a right triangle.
°
The angle that, together with yours, sums to 90°
- 1
Supplement = 180° − θ
180 − 35° = 145° - 2
Cofunction: sin(complement) = cos(θ)
cos(35°) = 0.8192Because the two angles share the same right-triangle sides, sin and cos swap roles. - 3
Complementary angle = 90° − θ
90 − 35° = 55°
How does this calculator work?
The complement of angle θ is 90° − θ. The two complementary angles form the acute angles of any right triangle. Trigonometric cofunction identities follow directly: sin(θ) = cos(90°−θ), tan(θ) = cot(90°−θ), and so on. Supplement = 180°−θ, explementary angle = 360°−θ.
Formula
How this is calculated
Two angles are complementary when they sum to exactly 90°. That means the complement of any angle θ is simply 90° − θ. They always appear together as the two non-right angles inside a right triangle: if one acute angle is θ, the other must be 90° − θ so all three angles sum to 180°.
The cofunction identities are a direct consequence of this relationship. In a right triangle with angle θ, the side opposite θ is the side adjacent to the complementary angle 90°−θ. So sin(θ) equals cos(90°−θ), and cos(θ) equals sin(90°−θ). The tangent of the complement is the reciprocal: tan(90°−θ) = 1/tan(θ), also written cot(θ). Memorising this pairing — sin↔cos, tan↔cot, sec↔csc — is the essence of the "co" prefix in cofunctions.
The supplementary angle (180°−θ) and the explementary (full-turn) angle (360°−θ) are included for reference, as they commonly appear in geometry and navigation problems alongside complementary angles.
Frequently asked questions
Technically 0° is the complement of 90° and vice versa, but neither is a proper interior angle of a non-degenerate right triangle. The calculator requires a strictly positive angle less than 90° for a meaningful result.
Complementary angles sum to 90° — they fit inside a right angle. Supplementary angles sum to 180° — they form a straight line. Both are useful; complementary angles appear most often in right-triangle trigonometry, supplementary angles in polygon interior-angle calculations.
They let you convert between sine and cosine (and their reciprocals) without a table. For example, sin(60°) = cos(30°). They are also essential in calculus for simplifying derivatives and integrals of trig functions.
Also known as
TG we-Calculate Editorial Team. (2026). Complementary Angles Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/complementary-angles-calculator
TG we-Calculate Editorial Team. "Complementary Angles Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/complementary-angles-calculator.
TG we-Calculate Editorial Team, "Complementary Angles Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/complementary-angles-calculator
@misc{wecalculate_complementary_angles_calculator, title = {Complementary Angles Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/complementary-angles-calculator}}, year = {2026}, note = {TG we-Calculate} }
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