Pythagorean Theorem Calculator

For any right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c². It only holds for triangles with a 90° angle.

Square both legs, add them, and take the square root: c = √(a² + b²). Enter the two legs in “find the hypotenuse” mode and the tool does this instantly.

Rearrange the formula: b = √(c² − a²). You subtract the known leg’s square from the hypotenuse’s square, then take the root. Use “find a leg” mode and enter the hypotenuse and the known leg.

Because it sits opposite the largest (right) angle. If you enter a hypotenuse shorter than or equal to a leg, no such right triangle exists and the square root would be of a negative number, so the tool flags it.

No — only right triangles. For triangles without a 90° angle you need the law of cosines, which generalises the Pythagorean theorem by adding a correction term.

Three whole numbers that satisfy a² + b² = c², such as 3-4-5, 5-12-13 and 8-15-17. Any multiple of a triple is also a triple, so 6-8-10 works too. Handy for constructing exact right angles.

For a right triangle the two legs are perpendicular, so the area is ½ × a × b. The perimeter is simply the sum of all three sides, a + b + c.

Yes. Enter decimals (a comma or a dot both work) in whatever unit you like — centimetres, metres, inches. The result comes out in the same unit, since the theorem is unit-independent.

Many right triangles have an irrational side — for legs of 1 and 1 the hypotenuse is √2 ≈ 1.41421. The tool shows six significant digits; round to whatever precision your problem needs.