Angle Of Right Triangle Calculator

Math

The Angle of a Right Triangle Calculator finds the two acute angles and the hypotenuse of a right triangle from the lengths of its two legs. It uses the inverse tangent of the opposite over the adjacent leg, with the second angle being its complement. The formula used is: angle = arctan(opposite ÷ adjacent); other angle = 90° − angle; hypotenuse = √(opposite² + adjacent²).

Formula

angle = arctan(opposite ÷ adjacent); other angle = 90° − angle; hypotenuse = √(opposite² + adjacent²)
  • The Angle of a Right Triangle Calculator finds both acute angles and the hypotenuse from the two legs and updates instantly when you change a value.
  • Formula: angle = arctan(opposite ÷ adjacent); other angle = 90° − angle; hypotenuse = √(opposite² + adjacent²)
  • Input definitions: • Opposite leg: the side across from the angle you want • Adjacent leg: the side next to that angle (the other leg of the right angle)
  • The two acute angles always add to 90°, since the right angle accounts for the remaining 90°.
  • Enter both legs in the same length unit; the hypotenuse comes out in that same unit.
  • Practical tip: swap which leg is 'opposite' to read the other angle directly as the primary result.

Example Calculation

Inputs
  • Opposite leg: 3
  • Adjacent leg: 4

With legs 3 and 4, the angle = arctan(3 ÷ 4) ≈ 36.87°, the other acute angle is 90° − 36.87° = 53.13°, and the hypotenuse is √(3² + 4²) = 5.

Frequently asked questions

How do you find an angle of a right triangle from its sides?
Take the inverse tangent of the opposite leg divided by the adjacent leg: angle = arctan(opposite ÷ adjacent). The other acute angle is simply 90° minus that.
Why do the two acute angles add to 90°?
Every triangle's angles sum to 180°. In a right triangle one angle is 90°, leaving 90° to be shared by the two acute angles.
What units should I enter?
Enter both legs in the same length unit. Angles are returned in degrees and the hypotenuse in your chosen unit.
How is the hypotenuse found?
By the Pythagorean theorem: hypotenuse = √(opposite² + adjacent²).
How accurate are the results?
Angles and the hypotenuse are computed exactly from the inputs and rounded only for display.