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Pythagorean Theorem Calculator

Solve a² + b² = c² for the hypotenuse or either leg of a right triangle.

Pythagorean theorem formulas

Theorema2 + b2 = c2
Hypotenusec = √a2 + b2
Missing lega = √c2 − b2

Where a, b = legs (the sides that form the right angle), c = hypotenuse (longest side)

Worked examples

  1. The legs of a right triangle are 5 and 12. Find the hypotenuse.

    1. c = √25 + 144 = √169

    Answer: c = 13

  2. A 10 ft ladder stands 6 ft from a wall. How high up the wall does it reach?

    1. h = √102 − 62 = √100 − 36 = √64

    Answer: 8 ft

  3. Is a triangle with sides 6, 8 and 10 a right triangle?

    1. 62 + 82 = 36 + 64 = 100 = 102 ✓

    Answer: Yes — the converse of the theorem confirms a right angle

Tips & common mistakes

  • Common Pythagorean triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25 (and multiples like 6-8-10).
  • Builders use 3-4-5 to check a corner is square.
  • It only works for right triangles — use the law of cosines otherwise.