Pythagorean Theorem Calculator
Solve a right triangle (a² + b² = c²).
- 100% free
- No sign-up
- Private — runs in your browser
- Instant results
Enter any two sides — leave the unknown one blank. c is the hypotenuse (longest side).
The Pythagorean theorem
For any right-angled triangle, the square of the hypotenuse (the longest side, opposite the right angle) equals the sum of the squares of the other two sides:
a² + b² = c²
Enter any two sides and this calculator solves for the third, then gives you the triangle's area and perimeter. Leave the side you want to find blank — c is always the hypotenuse.
Solving for each side
- Find the hypotenuse: c = √(a² + b²). The classic 3-4-5 triangle: √(9 + 16) = √25 = 5.
- Find a leg: a = √(c² − b²). The hypotenuse must be the longest side, so c has to be larger than the leg you already know — otherwise the triangle can't exist.
Where it's used
- Construction: the "3-4-5 rule" checks that a corner is a true right angle — measure 3 along one edge, 4 along the other, and the diagonal should be exactly 5.
- Navigation & maps: straight-line distance between two points is the hypotenuse of the horizontal and vertical differences.
- Screens & TVs: the advertised diagonal is the hypotenuse of the width and height.
FAQ
Does this work for any triangle?
No — only right triangles (one 90° angle). For other triangles you'd use the law of cosines or the law of sines.
What's a Pythagorean triple?
A set of three whole numbers that satisfy the theorem, like 3-4-5, 5-12-13, or 8-15-17. They're useful because all three sides come out as clean integers.
How do I find a leg when I know the hypotenuse and one leg?
Use a = √(c² − b²), subtracting the known leg's square from the hypotenuse's square before taking the root. Leave the leg you want blank and the tool solves it for you. The hypotenuse must be the longest side, so c has to be larger than the leg you already know.
Why do I get an error or no result?
If you enter a hypotenuse that's shorter than or equal to one of the legs, no valid right triangle exists, so the calculation can't return a real answer. Double-check that c is the longest side and that all values are positive.
Can I use it to find a diagonal distance or screen size?
Yes. Enter the horizontal and vertical differences as the two legs and the hypotenuse gives the straight-line distance. The same trick finds a screen's diagonal from its width and height.
Is this calculator free, and does it work on mobile?
Yes, it is completely free with no sign-up. It runs entirely in your browser so nothing is uploaded, and it works on phones, tablets, and desktops.