Hypotenuse
Calculate the hypotenuse of a right triangle from the two legs using the Pythagorean theorem. Free online hypotenuse solver for students, engineers, and DIY projects.
About This Calculator
The hypotenuse calculator uses the Pythagorean theorem to find the longest side of any right triangle. A right triangle has one 90-degree angle, and the side opposite that angle is called the hypotenuse. This calculator takes the two shorter sides (legs) and instantly computes the hypotenuse length.
The formula used is c = \u221a(a\u00b2 + b\u00b2), where c is the hypotenuse and a and b are the two legs. This fundamental geometric relationship has been known since ancient times and is one of the most widely used formulas in mathematics, engineering, and construction. Simply enter the lengths of both legs in any unit (inches, feet, centimeters, meters), and the calculator will return the hypotenuse in the same unit.
Who should use this calculator? Students learning geometry or trigonometry, carpenters and woodworkers calculating diagonal cuts, architects and engineers designing ramps or roof trusses, DIY enthusiasts planning home improvement projects, and anyone who needs to find the longest side of a right triangle quickly and accurately.
Real-world examples: Find the length of a ladder needed to reach a 10-ft wall when the base is 4 ft away (hypotenuse = 10.77 ft). Determine the diagonal of a rectangular TV screen (enter width and height as legs). Calculate the shortest distance between two points in a rectangular coordinate system. Measure the correct length for a roof rafter given the rise and run. The calculator is also useful for checking diagonal measurements in woodworking, verifying square corners, and solving navigation problems where the direct path between two points forms the hypotenuse of a right triangle.
Frequently Asked Questions
How do I calculate the hypotenuse of a right triangle?
Use the Pythagorean theorem: c = \u221a(a\u00b2 + b\u00b2), where a and b are the lengths of the two legs. Square both legs, add the results, and take the square root. For example, if side A = 3 and side B = 4, then hypotenuse = \u221a(9 + 16) = \u221a25 = 5.
What is the hypotenuse of a triangle?
The hypotenuse is the longest side of a right triangle, always opposite the 90\u00b0 right angle. It is the side that connects the two legs and is always longer than either leg.
Can I use this calculator for a 45-45-90 triangle?
Yes. For a 45-45-90 triangle (isosceles right triangle), enter the same value for both legs. The hypotenuse will equal leg \u00d7 \u221a2. For example, legs of 5 each give a hypotenuse of 5 \u00d7 1.414 = 7.07.
Will this work for any right triangle measurement unit?
Yes. The calculator is unit-agnostic -- enter measurements in any unit (inches, feet, cm, meters) and the hypotenuse will be in the same unit. Just ensure both legs use the same unit.
How do I find one leg if I know the hypotenuse and the other leg?
Rearrange the Pythagorean theorem: a = \u221a(c\u00b2 - b\u00b2). Subtract the square of the known leg from the square of the hypotenuse, then take the square root. Our Missing Side of a Right Triangle calculator handles this case.
What practical situations use hypotenuse calculations?
Hypotenuse calculations are used in construction (roof rafters, stair stringers), navigation (shortest distance), carpentry (diagonal cuts), engineering (ramp lengths), and everyday DIY projects like finding the right ladder length.
Is this tool free to use?
Yes, all calculators on Calculy are completely free to use with no registration or download required.