Complementary Angles Calculator

Enter one angle to find its complement — the angle that, added to it, totals exactly 90 degrees.

Quick Facts

Definition
Complementary angles are two angles whose measures sum to 90°
Each one must be acute (strictly between 0° and 90°) — they don't need to be adjacent.

Your Results

Calculated
Complementary angle
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90° minus your angle
In radians
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Complement converted to radians
Degrees-minutes-seconds
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Complement in DMS notation
Supplementary angle
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180° minus your angle (bonus)

Ready

Enter an angle between 0° and 90°, then press Calculate.

Understanding Complementary Angles

This calculator finds the complement of an angle you already know. Two angles are complementary when their measures add up to exactly 90 degrees — a right angle. Given one angle, the complement follows from a single subtraction.

The formula

For a known angle A, the complement is:

  • Complement = 90° − A (in degrees), or Complement = π/2 − A (in radians)

Because a complement must itself be a positive angle, this only works for values of A strictly between 0° and 90° — in other words, A must be acute. If A is 0°, 90°, or greater, no positive complementary angle exists.

Complementary vs. supplementary angles

Complementary angles sum to 90°; supplementary angles sum to 180° (a straight line). The two terms are easy to mix up but answer different questions, so this calculator reports both the complement and the supplement of your angle. An angle's supplement is always exactly 90° more than its complement.

Degrees, radians, and DMS notation

Enter your angle in whichever unit you're working with — decimal degrees or radians — and the result is shown back in degrees, radians, and degrees-minutes-seconds (DMS) notation. DMS is the traditional format used in surveying and navigation, where each degree splits into 60 minutes and each minute splits into 60 seconds.

Checking your result

A quick sanity check: add your original angle to the complement shown — the two should sum to exactly 90°. If your angle is less than 45°, the complement will be greater than 45°, and vice versa; only a 45° angle is its own complement.

Frequently Asked Questions

What are complementary angles?
Two angles are complementary when their measures add up to exactly 90 degrees. For example, a 30-degree angle and a 60-degree angle are complementary because 30 + 60 = 90. The angles do not need to be adjacent (touching) — they only need to sum to a right angle.
How do I find the complement of an angle?
Subtract the angle from 90 degrees. If an angle measures 35 degrees, its complement is 90 − 35 = 55 degrees. This only works for angles between 0 and 90 degrees, since a complementary partner angle must also be positive.
What is the difference between complementary and supplementary angles?
Complementary angles sum to 90 degrees (a right angle), while supplementary angles sum to 180 degrees (a straight angle). A single angle can have both a complement and a supplement at the same time — a 35-degree angle has a 55-degree complement and a 145-degree supplement.
Can an angle greater than 90 degrees have a complement?
No. A complement is defined as 90 degrees minus the given angle, and it must itself be a positive angle. Only angles strictly between 0 and 90 degrees — acute angles — have a valid positive complement.

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