◺ Pythagorean Theorem Calculator
Find the missing side of a right triangle. Solve for the hypotenuse or either leg using a² + b² = c².
Known Sides
Result
Hypotenuse (c)
5
3² + 4² = 5²
Side a
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Side b
–
Hypotenuse c
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The Pythagorean Theorem
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
c = √(a² + b²)
a = √(c² − b²)
b = √(c² − a²)
c = √(a² + b²)
a = √(c² − b²)
b = √(c² − a²)
Frequently Asked Questions
What is a classic example of the Pythagorean theorem?
The 3-4-5 triangle is a classic example: 3² + 4² = 9 + 16 = 25 = 5². Any multiple of 3-4-5 (like 6-8-10) also works.
What if the hypotenuse is shorter than a leg?
The hypotenuse must always be the longest side of a right triangle. If you enter a hypotenuse shorter than or equal to a leg, the calculator will show a validation error since no valid triangle exists.
Does this only work for right triangles?
Yes. The Pythagorean theorem applies specifically to right triangles — triangles with one 90° angle. For other triangles, use the Law of Cosines instead.