Pythagorean Theorem Calculator
Find the missing side of any right triangle — a² + b² = c².
The Pythagorean Theorem Calculator finds the missing side of a right triangle: give it two legs and it returns the hypotenuse, or give it the hypotenuse and one leg and it returns the other. The formula, a² + b² = c², is shown with your numbers substituted in.
The theorem is the most-used piece of geometry in the real world — construction workers square corners with 3-4-5 measurements, carpenters check diagonals, and anyone computing screen diagonals, ladder clearances or roof slopes is doing Pythagoras. The calculator also celebrates when your sides form a Pythagorean triple (all whole numbers, like 3-4-5).
Results are exact to four decimal places with an option for further precision. Everything runs locally in your browser.
Hypotenuse c
5.0000
3² + 4² = c²
Pythagorean triple: all three sides are whole numbers! 🎉
a² + b² = c² — valid only for right triangles. The calculator also checks for Pythagorean triples (3-4-5, 5-12-13…) when sides are whole numbers.
How to use the Pythagorean Theorem Calculator
- Choose whether you need the hypotenuse or a missing leg.
- For the hypotenuse: enter the two legs (a and b).
- For a leg: enter the hypotenuse and the known leg.
- Read the missing side and the formula.
- Check for the triple celebration when all sides are whole numbers.
Frequently asked questions
When does the Pythagorean theorem apply?
Only to right triangles — triangles with a 90° angle. The hypotenuse is always the side opposite the right angle and the longest side. For other triangles you need the law of cosines.
What are Pythagorean triples?
Whole-number solutions like 3-4-5, 5-12-13 and 8-15-17 where a² + b² = c² exactly. Builders exploit them to check right angles with integer measurements.
How is this used in everyday work?
Squaring foundations (measure 3 and 4 along the walls, the diagonal must be 5), sizing TV screens from width and height, computing roof lengths from rise and run, and any time you need a straight-line distance across a right angle.
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