Online Hypotenuse Calculator
Find the longest side of a right triangle instantly using the Pythagorean theorem (a² + b² = c²) with detailed step-by-step solutions.
Understanding Right Triangles
Master the core concepts of geometry and the Pythagorean theorem.
The Formula
The Pythagorean equation is written as a² + b² = c². To solve for c (the hypotenuse), you take the square root of the sum of a² and b², making it c = √(a² + b²).
Always the Longest
The hypotenuse is strictly the longest side of a right triangle. If you calculate a hypotenuse that is shorter than either of your legs, you\'ve made an error in calculation.
Real-world Use
This formula is used daily in architecture, construction, navigation, and surveying to find the shortest straight-line distance between two points.
Frequently Asked Questions
What is the hypotenuse?
The hypotenuse is the longest side of a right-angled triangle. It is always the side that is opposite the right angle (the 90-degree angle).
What is the Pythagorean theorem?
The Pythagorean theorem is a fundamental relation in geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides: a² + b² = c².
Does this work for all triangles?
No, the Pythagorean theorem (and this calculator) only works for right-angled triangles—triangles where one angle is exactly 90 degrees. For other triangles, you would need to use the Law of Cosines.
What happens if I only know the hypotenuse and one leg?
If you know the hypotenuse (c) and one leg (let's say a), you can rearrange the formula to find the other leg (b): b = √(c² - a²). Our current calculator is specifically designed to find the hypotenuse when both legs are known.
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