🔺Pythagorean Theorem Calculator
Solve for any side of a right triangle given the other two, using a² + b² = c².
Free Pythagorean Theorem Calculator
Our free Pythagorean theorem calculator solves for any missing side of a right triangle using a² + b² = c². Enter exactly two of the three sides — the two legs (a and b) or a leg and the hypotenuse (c) — and the third side is calculated instantly, with a scaled diagram showing the triangle.
Whether you're solving a geometry homework problem, checking a construction measurement, or working out the diagonal of a rectangle, this tool gives you the exact answer along with the formula and substitution shown step by step.
The Pythagorean theorem only applies to right triangles, where one angle is exactly 90°, and the hypotenuse is always the longest side, opposite that right angle. No sign-up, no downloads — everything runs instantly in your browser.
About the Pythagorean Theorem Calculator
Features
Solve any side
Enter any two sides — both legs, or a leg and the hypotenuse.
Live diagram
A scaled right-triangle diagram updates as you type, with the solved side highlighted.
Area included
See the triangle's area alongside the three side lengths.
Step-by-step working
See the exact formula and substitution used to reach the result.
Frequently Asked Questions
What is the Pythagorean theorem?
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) equals the sum of the squares of the two legs (a and b): a² + b² = c².
Which side is the hypotenuse?
The hypotenuse is always the longest side of a right triangle, located opposite the 90° angle.
Can I solve for a leg instead of the hypotenuse?
Yes. Enter one leg and the hypotenuse, and the calculator solves for the missing leg using b = √(c² − a²).
Does this only work for right triangles?
Yes, the Pythagorean theorem only applies to right triangles — triangles with exactly one 90° angle.
Why does the hypotenuse have to be longer than each leg?
Because the hypotenuse is the longest side of a right triangle by definition; if a given 'hypotenuse' value were shorter than a leg, no valid right triangle exists.
Can I use decimal or fractional side lengths?
Yes, the calculator accepts any positive decimal value for the side lengths.
What real-world problems use the Pythagorean theorem?
Common uses include finding a ladder's required length, a TV or monitor's diagonal size, the diagonal of a rectangular room, and distances in navigation or construction.
Does the calculator show the triangle's area?
Yes, once both legs are known, the area (½ × a × b) is shown alongside the side lengths.
How many sides do I need to enter?
Enter exactly two of the three sides; the calculator solves for the third automatically.
Is this calculator free to use?
Yes, the Pythagorean theorem calculator is completely free with no sign-up, and all calculations run instantly in your browser.