Pythagoras in one line
The square of the hypotenuse equals the squares of the other two sides added together, written a squared plus b squared equals c squared.
To find the hypotenuse, square both shorter sides, add them and take the square root. To find a shorter side, square the hypotenuse and the known side, subtract, then take the square root.
Worked example
A triangle with shorter sides of 3 cm and 4 cm has a hypotenuse of 5 cm, because 9 + 16 = 25.
Its area is 3 x 4 / 2 = 6 cm², its perimeter is 12 cm, and its angles are 36.8699 and 53.1301 degrees beside the right angle.
What the calculator refuses
The hypotenuse is always the longest side, so it must be longer than the shorter side you enter. Equal or shorter values are rejected.
Zero and negative lengths are refused too, because a right-angled triangle needs two positive shorter sides.
Inputs for the right angle triangle calculator
What do you want to find?
Choose the hypotenuse, or one of the shorter sides. The boxes below change to match.
First and second shorter side
The two sides that meet at the right angle, sometimes called the legs.
Hypotenuse and known shorter side
The longest side and the shorter side you already measured. The hypotenuse must be the longer of the two.
Measurement unit
The unit your sides are in. The missing side and perimeter come back in the same unit.
CALCULATOR QUESTIONS
Right angle triangle calculator questions
How do I find the hypotenuse?
Square both shorter sides, add them, then take the square root. For 3 and 4 that gives 5.
How do I find a shorter side?
Square the hypotenuse and the known shorter side, subtract the smaller from the larger, then take the square root.
Why must the hypotenuse be the longest side?
It lies opposite the right angle, which is the widest angle in the triangle, so the side facing it is the longest.
Are the angles in degrees?
Yes. The two angles beside the right angle are shown in degrees and always add up to 90.