Pythagorean Theorem Calculator
Find the missing side of a right triangle using a² + b² = c². Free and instant — results update as you type, with the full working shown, and nothing leaves your browser.
The legs a and b are the two sides that form the right angle; c is the hypotenuse (the longest side, opposite the right angle). Any unit works — the answer is in the same unit.
How to use the Pythagorean theorem calculator
- Choose the side to solve for. Pick Hypotenuse c if you know both legs, or Leg a / Leg b if you know one leg and the hypotenuse.
- Enter the two known sides. Type the lengths in any unit (cm, m, inches, feet…). Decimals are fine, and the result updates instantly as you type.
- Read the answer and the steps. You get the missing side, the triangle's area, perimeter and both acute angles, plus the full a² + b² = c² working ready to copy into your homework.
About this tool
The Pythagorean theorem states that in every right triangle the square of the hypotenuse equals the sum of the squares of the two legs: a² + b² = c². This free Pythagorean theorem calculator applies that formula in both directions — it finds the hypotenuse from two legs (c = √(a² + b²)) or a missing leg from the other leg and the hypotenuse (a = √(c² − b²)). Alongside the missing side it computes the triangle's area (½ · a · b), its perimeter, and the two acute angles, so one entry gives you the complete solved triangle.
It is a handy checker for geometry and trigonometry homework, and just as useful in the real world: carpenters use 3-4-5 triangles to square corners, builders size ladders and roof rafters with it, and screen sizes are simply the hypotenuse of the display's width and height. Every calculation runs locally in your browser with double-precision math — nothing you type is uploaded, stored or logged.
Frequently asked questions
What is the Pythagorean theorem?
For any right triangle with legs a and b and hypotenuse c, the theorem says a² + b² = c². It lets you compute any one side when the other two are known, and it only holds when the triangle contains a 90° angle.
Which side is the hypotenuse?
The hypotenuse is the side opposite the right angle and is always the longest side of a right triangle. The other two sides — the ones that meet at the 90° corner — are called the legs. That is also why the calculator rejects a hypotenuse that is not longer than the known leg.
Can I use this for a triangle without a right angle?
No. The Pythagorean theorem only applies to right triangles. For other triangles you need the law of cosines (c² = a² + b² − 2ab·cos C), which reduces to the Pythagorean theorem when C = 90°.
How are the angles calculated?
Once all three sides are known, the acute angles follow from basic trigonometry: α = arcsin(a / c) and β = arcsin(b / c). Together with the 90° right angle they always sum to 180°.