📐 Pythagorean Theorem Calculator
Find any missing side of a right triangle using a² + b² = c². Choose what you want to find, enter the two known sides, and get the answer with full step-by-step working.
Enter sides a and b to find hypotenuse c.
Pythagorean Theorem
Worked Example — Find c with a=3, b=4
Frequently Asked Questions
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c². It was named after the ancient Greek mathematician Pythagoras.
Pythagorean triples are sets of three positive integers (a, b, c) that satisfy a² + b² = c². The most famous is (3, 4, 5). Others include (5, 12, 13), (8, 15, 17), and (7, 24, 25). Any multiple of a triple is also a triple — e.g. (6, 8, 10).
It is used in construction (checking square corners), navigation (finding shortest distances), architecture, computer graphics (calculating pixel distances), and physics (resolving vector components). Carpenters use the 3-4-5 rule to ensure right angles.
Square both known sides, add them together, then take the square root. For example, a=6 and b=8: c = √(36+64) = √100 = 10.
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