Pythagorean Theorem Calculator
Calculate the hypotenuse or a leg of a right triangle (a² + b² = c²).
Tip: Only valid for right triangles (with one 90° angle).
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About this digital tool
The Pythagorean theorem calculator finds the missing side of a right triangle. Choose whether you are looking for the hypotenuse (c) or a leg, enter the two known values and get the result instantly. If the hypotenuse value is smaller than the leg, the calculator warns you of the error.
The formula is a² + b² = c². For legs 3 and 4: c = √(9 + 16) = √25 = 5. If the hypotenuse 13 and one leg 5 are known, the other leg is √(169 − 25) = √144 = 12. The theorem is used to measure diagonals, to check right angles in construction, for stairs and roofs, and for distances in the plane.
How to use
- Choose what you are looking for: the hypotenuse or a leg.
- Enter the two known values.
- See the calculated result.
Frequently asked questions
How do I find a leg when I know the hypotenuse?
Use a = √(c² − b²): subtract the square of the known leg from the square of the hypotenuse, then take the square root.
How do I find the hypotenuse of a right triangle?
Square both legs, add them and take the square root: c = √(a² + b²). E.g. for a = 6 and b = 8, c = √100 = 10.
What are Pythagorean triples?
They are triples of whole numbers that satisfy a² + b² = c². The best known are 3-4-5, 5-12-13 and 8-15-17 (because 64 + 225 = 289).
How do I calculate the diagonal of a rectangle with the Pythagorean theorem?
The diagonal is the hypotenuse of the triangle formed by the length and width. For a 6 × 8 rectangle the diagonal is √(36 + 64) = 10.