Pythagorean theorem and right triangle calculator
Calculate the hypotenuse or a leg with the Pythagorean theorem and see the angles, area, perimeter and height of the right triangle, with a drawing and step-by-step work.
How to useHypotenuse, legs and angles
Fill in two sides and leave the third blank.
Available in: 
Pythagorean theorem and right triangle calculator: what it is for
Fill in two sides of the right triangle and the calculator finds the third with the Pythagorean theorem, showing the work. It also calculates the two acute angles, the area, the perimeter and the height to the hypotenuse, with a drawing of the triangle.
How to use
- Type two sides.
- Leave the unknown side blank.
- See the result and the steps.
When to use it
- Solving math exercises.
- Finding the diagonal of a room or screen.
- Measuring roofs, ramps and stairs.
Frequently asked questions
What does the Pythagorean theorem say?
In every right triangle, the square of the hypotenuse equals the sum of the squares of the legs: c² = a² + b². With legs of 3 and 4, the hypotenuse is √(9 + 16) = 5.
How do I find a leg?
Subtract the square of the known leg from the square of the hypotenuse and take the square root: b = √(c² − a²). The hypotenuse must be longer than the leg.
How are the angles calculated?
With the arcsine or arctangent: the angle opposite leg a is arctan(a ÷ b). The two acute angles always add up to 90°.
Is it really free?
Yes, 100% free. No sign-up, no subscription and no usage limits. All Tools123 tools are free and run right in your browser.