Find the complement (90° − θ) and supplement (180° − θ) of any angle. See cofunction identities, trig values of both angles, and the explement. Includes angle pair tables and visual bars.
The **Complementary & Supplementary Angles Calculator** instantly finds the complement, supplement, and explement of any angle you enter. The complement is the angle that adds to yours to make 90°, the supplement adds to 180°, and the explement (conjugate angle) completes a full 360° rotation.
Enter an angle in degrees, radians, or gradians, and the calculator displays the complementary and supplementary angles along with their trigonometric values. By computing sin, cos, and tan for both the original angle and its complement, the tool demonstrates the cofunction identities in action — for example, sin(θ) = cos(90° − θ) and tan(θ) = cot(90° − θ). These identities are fundamental in trigonometry and arise frequently in proofs, simplifications, and real-world applications.
Complementary angles appear everywhere in geometry: the two acute angles in a right triangle are always complementary; if a ramp makes a 30° angle with the ground, the angle with the vertical wall is 60°. Supplementary angles arise with parallel lines and transversals, in polygon interior angle sums, and in physics when analysing reflection angles.
The tool also includes a pairs table showing ten standard complementary-supplementary angle combinations, a stacked bar illustrating how the angle and its complement sum to exactly 90°, and an expandable cofunction identity reference with live computed values.
Complementary & Supplementary Angles Calculator helps you avoid repetitive setup mistakes when solving trigonometric and coordinate-geometry problems. Instead of recalculating conversions, signs, and edge cases by hand, you can test inputs immediately, inspect intermediate values, and confirm final answers before submitting work or using numbers in downstream calculations. It surfaces key outputs like Angle θ (degrees), Complement (90° − θ), Supplement (180° − θ) in one pass.
Complement = 90° − θ (exists when 0° ≤ θ ≤ 90°). Supplement = 180° − θ (exists when 0° ≤ θ ≤ 180°). Explement = 360° − θ. Cofunction identity: sin(θ) = cos(90° − θ), cos(θ) = sin(90° − θ), tan(θ) = cot(90° − θ).
Result: Computed from the entered values
Using v=30, the calculator returns Computed from the entered values. This example mirrors the calculator's live computation flow and is useful for checking manual steps and unit handling.
This calculator is tailored to complementary & supplementary angles calculator workflows, including common input modes, unit handling, and special-case behavior. It is designed for fast checking during homework, exam preparation, technical drafting, and coding tasks where trigonometric consistency matters.
Use the primary result together with supporting outputs to verify direction, magnitude, and validity. Cross-check against known identities or geometric constraints, and confirm that angle ranges, sign conventions, and domain restrictions are satisfied before using the numbers elsewhere.
A reliable way to improve is to solve once manually, then verify with the calculator and explain any mismatch. Repeat this on varied examples and edge cases. The built-in preset scenarios for quick trials, comparison tables for side-by-side validation, visual cues that make trends and quadrants easier to read help you build pattern recognition and reduce sign or conversion errors over time.
Two angles are complementary when they add up to 90° (a right angle). For example, 30° and 60° are complementary. Each angle is the complement of the other.
Two angles are supplementary when they add up to 180° (a straight angle). For example, 120° and 60° are supplementary.
No. Since the complement of θ is 90° − θ, any angle greater than 90° would produce a negative complement, which is not a valid angle.
The explement is 360° − θ. Together with the original angle, it completes a full revolution. It's sometimes called the conjugate or explementary angle.
Cofunction identities state that the sine of an angle equals the cosine of its complement: sin(θ) = cos(90°−θ), and vice versa. "Co"-sine literally means "complement's sine."
By definition, yes. Both the original angle and its complement (or supplement) should be positive. If the calculation yields a negative, the relationship does not exist for that angle.