Pythagorean Theorem Calculator (hypotenuse)
Find the hypotenuse of a right triangle from its two legs.
Result
Hypotenuse (c)
5.0000
How it works
The Pythagorean theorem ties together the three sides of a right triangle: the square of the hypotenuse equals the sum of the squares of the two legs, a² + b² = c². Enter the two legs and this calculator returns the hypotenuse c = √(a² + b²). The most famous instance is 3-4-5: 9 + 16 = 25. Such whole-number triples have been used since antiquity to lay out perfect right angles with nothing but a knotted rope — builders still use the trick today. The theorem hides in everyday measurements: the diagonal of a TV screen or a room, the reach of a ladder against a wall, the straight-line distance between two points on a map (the distance formula is Pythagoras in coordinates). It only holds for right triangles — for other shapes, the law of cosines generalises it.
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Frequently asked questions
What is the Pythagorean theorem?
In a right triangle, a² + b² = c², where c is the hypotenuse.
What are the legs and the hypotenuse?
The legs are the two sides forming the right angle; the hypotenuse is the longest side, opposite it.
How do I find a missing leg instead of the hypotenuse?
Rearrange the theorem: a = √(c² − b²). Square the hypotenuse, subtract the square of the known leg, and take the square root of what remains.
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