Pythagorean Theorem Calculator
Calculate missing side of right triangle using a²+b²=c²
About the Pythagorean Theorem Calculator
The Pythagorean theorem — a² + b² = c² — relates the three sides of a right triangle, and this calculator solves for whichever side you are missing. Tell it which side to find, enter the other two, and it returns the answer with the algebra and a triangle diagram.
Students lean on it throughout geometry and trigonometry; in practice, carpenters, builders, and DIYers use it to check that corners are square and to find diagonal lengths. Because it solves for any side — not just the hypotenuse — it handles the full range of right-triangle problems, and the visual diagram makes clear which side is which.
How to Use the Pythagorean Theorem Calculator
- Choose which side to solve for: side a, side b, or the hypotenuse c.
- Enter the two sides you know.
- Read the calculated length of the missing side.
- Review the formula derivation and the triangle diagram that highlights the side you solved for.
Why Use ToolForge’s Pythagorean Theorem Calculator
- It solves for any of the three sides, not just the hypotenuse, covering every right-triangle case.
- It includes a triangle diagram that updates to show which side you are finding, anchoring the algebra visually.
- It shows the full derivation, from squaring the known sides to the final square root.
- It runs entirely in your browser, free and private.
Frequently Asked Questions
What is the Pythagorean theorem?
For a right 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. It only applies to right triangles.
How do I find a leg instead of the hypotenuse?
Rearrange the formula: a = √(c² − b²). Choose to solve for side a or b, enter the hypotenuse and the other leg, and the calculator subtracts and takes the square root for you.
How is this used to check a square corner?
Builders use the 3-4-5 rule: if a corner's two sides measure 3 and 4 units, the diagonal should be exactly 5 for a true right angle. You can verify any such measurement by solving for the hypotenuse here.
Does the theorem work for any triangle?
No — it applies only to right triangles, those with a 90-degree angle. For triangles without a right angle you need the law of cosines or law of sines instead. This calculator assumes a right triangle in every mode.
