Math
Hypotenuse Calculator
Calculate the hypotenuse or any missing side of a right triangle using the Pythagorean theorem. Choose which side to solve for and enter the other two.
Enter two sides to find the third.
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Pythagorean Theorem Formulas
Find Hypotenuse (c)
c = √(a² + b²)
Find Side a
a = √(c² − b²)
Find Side b
b = √(c² − a²)
Practical Applications
Construction & carpentry: The 3-4-5 rule (a right triangle with sides 3, 4, 5) is used to check or create perfect 90° corners in foundations, tiling, and framing.
Screen & room diagonals:A TV advertised as 65" has a diagonal of 65 inches — use the theorem with the aspect ratio to find actual width and height.
Distance calculations: The straight-line distance between two points on a grid (x₁, y₁) and (x₂, y₂) is √((x₂−x₁)² + (y₂−y₁)²) — the Pythagorean theorem in coordinate form.
Frequently asked questions
What is the Pythagorean theorem?
The Pythagorean theorem states that in any right triangle, the square of the hypotenuse (c) equals the sum of the squares of the two legs (a and b): c² = a² + b². It is one of the most fundamental results in geometry, attributed to the ancient Greek mathematician Pythagoras.
What is the hypotenuse?
The hypotenuse is the longest side of a right triangle — the side opposite the right angle (90°). If you label the legs a and b, the hypotenuse c satisfies c = √(a² + b²). It is always longer than either individual leg.
Does the Pythagorean theorem only work for right triangles?
Yes. The Pythagorean theorem applies exclusively to right triangles (triangles with one 90° angle). For non-right triangles, the Law of Cosines provides the generalisation: c² = a² + b² − 2ab·cos(C).
What are real-world applications of the Pythagorean theorem?
Applications include: measuring the diagonal of a screen or room, calculating the straight-line distance between two GPS coordinates, engineering and construction (roof pitch, staircase design, cable runs), computer graphics (distance between two points), and navigation.
Can the side lengths be decimal numbers?
Yes. The Pythagorean theorem works for any positive real numbers — whole numbers, fractions, and decimals are all valid. The classic integer examples (Pythagorean triples like 3-4-5, 5-12-13) are special cases that produce whole-number results.