📐 Pythagorean Theorem Calculator

a² + b² = c² — Enter two values, leave the unknown blank.

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The Pythagorean Theorem

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (longest side) equals the sum of squares of the other two sides.

a² + b² = c²
Hypotenuse c = √(a² + b²)
Leg a = √(c² − b²)

Pythagorean Triples (Perfect Integer Solutions)

3-4-5
9+16=25 ✓
5-12-13
25+144=169 ✓
8-15-17
64+225=289 ✓
7-24-25
49+576=625 ✓

Frequently Asked Questions

What is the hypotenuse of a 3-4-? triangle? ▼
c = √(3² + 4²) = √(9+16) = √25 = 5. The classic 3-4-5 Pythagorean triple.
Who discovered the Pythagorean theorem? ▼
While named after Pythagoras (570–495 BC), the theorem was known in Babylon 1000 years earlier. Pythagoras is credited with the first proof.
Is the Pythagorean theorem only for right triangles? ▼
Yes. The theorem only applies to right triangles (those with a 90° angle). For other triangles, use the law of cosines: c² = a² + b² − 2ab·cos(C).