Pythagorean Theorem Calculator
Calculate the hypotenuse or a leg of a right triangle using the Pythagorean theorem. Fill in two of the three sides and leave the third at 0, and the calculator works out the rest.
How to use the Pythagorean theorem calculator
- Enter the two sides you know in a right triangle.
- Leave the field you don't know at 0 — the calculator automatically works out this value.
- If you fill in all three fields, the calculator instead checks whether the measurements actually satisfy the Pythagorean theorem.
The Pythagorean theorem
Worked example: a right triangle with legs of 3 and 4 has a hypotenuse of √(3² + 4²) = √25 = 5. This is the best-known Pythagorean triple, and was in practical use long before Pythagoras — Egyptian surveyors used a rope with twelve knots to set out right angles.
In a right triangle, a and b are the two legs (the sides that meet at the right angle), while c is the hypotenuse — the side opposite the right angle. The hypotenuse is always the longest side in a right triangle.
If you know two of the sides, you can solve the equation for the third: c = √(a² + b²) to find the hypotenuse, or a = √(c² − b²) to find a leg.
Frequently asked questions
What is the Pythagorean theorem used for in practice?
The Pythagorean theorem is used to find distances, check whether a corner is 90 degrees (for example in construction and carpentry), and calculate diagonals in rectangles and other practical measurements.
Can I use this for triangles other than right triangles?
No, the Pythagorean theorem only applies to right triangles — triangles with one corner at exactly 90 degrees. For other triangles you need other methods, such as the law of cosines.
What happens if I fill in all three fields?
Then the calculator uses the numbers to check whether they actually satisfy the Pythagorean theorem, i.e. whether a² + b² actually equals c². This is useful if you want to verify whether a triangle is a right triangle.