Complementary Angles Calculator (90° − θ in degrees and radians)

Understanding the complementary angles calculator — concept and principle

This calculator finds the complement of an angle, the angle that adds with it to 90°, in degrees and radians. It also shows the sine–cosine co-function link and the supplement of the same angle. Use it for geometry and trigonometry homework, right-triangle problems or quick checks.

Complementary angles fill a right angle, so the sine of one is the cosine of the other.

How it is calculated

Complement = 90° − θ (or π/2 − θ in radians)

Radians = degrees × π ÷ 180

sin θ = cos(90° − θ)

Supplement = 180° − θ

Only angles strictly between 0° and 90° have a positive complement.

The principle

The angles of a triangle add up to 180°. In a right triangle one angle is 90°, so the other two must add up to 90°: they are complementary. The side opposite one acute angle is the side adjacent to the other, which is why the sine of an angle equals the cosine of its complement, and tangent equals the cotangent of the complement. The "co" in cosine, cotangent and cosecant comes from "complement".

Worked example

Default inputs: θ = 35°, degrees.

Your angle in degrees: 35.
Complement = 90 − 35 = 55°.
In radians: 55 × π ÷ 180 = 0.959931 rad.
sin 35° = cos 55° = 0.573576.
Supplement of the same angle = 180 − 35 = 145°.

Each point is the calculator re-run with only “Angle θ” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Angle θ	Complement (°)
8.75	81.25
17.5	72.5
26.2	63.75
35	55
43.8	46.25
52.5	37.5
70	20

How to read the result

Two complementary angles together make a right angle; if your answer is negative, the original angle was more than 90° and has no complement. Do not confuse complements (sum 90°) with supplements (sum 180°). In a right triangle, knowing one acute angle immediately gives the other.

Common mistakes

Subtracting from 180° instead of 90°.
Mixing degrees and radians.
Expecting a complement for an obtuse angle.
Swapping sine and cosine in the co-function identity.

Keep in mind: Results are rounded to six significant digits. For exact work, keep values such as π/2 in symbolic form.

Frequently asked questions

What is the complement of 35°?

55°, since 35° + 55° = 90°.

What is the difference between complementary and supplementary angles?

Complementary angles add up to 90°, supplementary angles to 180°.

Why does sin θ equal cos(90° − θ)?

In a right triangle the side opposite one acute angle is adjacent to the other.

Sources: OpenStax, Precalculus 2e (2021), §5.1 Angles and §5.4 Right Triangle Trigonometry

Checked 9 Nov 2026. OpenStax, Precalculus 2e (2021), Chapter 5 Key Concepts — §5.4 (any two complementary angles can be the two acute angles of a right triangle; cofunction identities) and §5.1 (θ/180 = θᵣ/π); OpenStax, Contemporary Mathematics (2023), §10.2 Angles (definition of complementary angles).

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