Two complementary angles add up to a right angle: 90°. If you know one of them, this calculator finds the other. For example, an angle of 28° needs another 62° to complete a right angle.
This comes up when finding the two acute angles in a right triangle or checking a corner divided into two parts. The angles do not have to sit next to each other to be complementary; their sum is what matters.
For an ordinary pair of positive complementary angles, the starting angle must be greater than 0° and less than 90°. This form performs the subtraction for other values too, so check whether the result makes sense for your diagram.
| Quantity | Meaning |
|---|---|
| θ, the known angle | The angle you already know, measured in degrees. This form does not convert radians. |
| Complement | The angle needed to reach 90°. It has the same unit as the input. |
Suppose a right triangle has one acute angle of 37.5°. Its other acute angle is 90° − 37.5° = 52.5°. Checking gives 37.5° + 52.5° = 90°. Together with the triangle’s right angle, the three angles total 180°.
For a second check, enter 45°. The answer is also 45°, showing that complementary angles can be equal. Entering 90° gives 0°; this is a boundary value, rather than a pair of positive acute angles.
Suppose a question says that one of two complementary angles is twice the other. Call the smaller angle x. The larger is 2x, so x + 2x = 90°. Dividing by three gives x = 30° and 2x = 60°. You can enter either number into this calculator to check the partner angle, but the ratio equation is the step that determines the original angle.
For an angle of 24° 15′, convert the minutes first: 15 ÷ 60 = 0.25°. Enter 24.25, which gives 65.75°. To write the answer in degrees and minutes, convert the decimal part back: 0.75 × 60 = 45′. The complement is therefore 65° 45′. This extra conversion keeps the subtraction consistent.
Use this calculation when a problem explicitly gives a right angle or says two angles are complementary. A drawing that merely looks square is not enough evidence: look for a right-angle marker or a stated measurement.
In a right triangle, the two angles other than the right angle are complementary because every triangle has an angle sum of 180°. For a straight line split into two angles, use 180° minus the known angle instead. That is a supplementary-angle problem.
Yes. If the two angles are equal, each is 90° ÷ 2 = 45°. A right triangle with two 45° angles is also isosceles.
No. Adjacent describes their position: they share a vertex and a side without overlapping. Complementary describes their total. Two adjacent angles can be complementary, but they need not be.
Check the question and the input. A known angle greater than 90° cannot have a positive complement in ordinary elementary geometry. If the question refers to a straight angle, you may need a supplement instead.
Add the two angles, using a common unit. If the total is 90°, they are complementary. If it is 180°, they are supplementary. If neither total is correct, check for a copied measurement, a unit conversion or a different geometric relationship.
Yes. The relationship works in either direction. If 22° is complementary to 68°, then 68° is complementary to 22°. Subtracting either one from 90° recovers the other, so the calculator can also check an answer you already have.
For angles measured in degrees, sin(θ) = cos(90° − θ). If θ is 30°, its complement is 60° and both sin(30°) and cos(60°) equal 0.5. This relationship can help check a right-triangle exercise. It uses complementary angles, not supplementary angles, and does not mean that sine and cosine have the same value at every original angle.
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