Hypotenuse Calculator – Guide & Formulas
Calculate the hypotenuse (c) of a right triangle instantly. Supports decimal outputs, square root simplify steps, and finds missing leg lengths.
Instantly find the hypotenuse or a missing leg of a right triangle using the Pythagorean theorem. Enter the lengths of the two legs to get the step-by-step solution.
Key Takeaway
Use the free Hypotenuse Calculator to calculate the hypotenuse (c) of a right triangle instantly. supports decimal outputs, square root simplify steps, and finds missing leg lengths. Get instant results with step-by-step explanations.
How to Use the Hypotenuse Calculator
- To find the hypotenuse, enter the lengths of both perpendicular legs (Side a and Side b).
- To find a missing leg, enter the known leg and the hypotenuse.
- Observe the precise decimal result and the step-by-step equation expansions.
The Formula
Variable Definitions
- a, b: The lengths of the perpendicular sides (legs)
- c: The length of the hypotenuse
Finding the Hypotenuse of a 5-12 Right Triangle
A carpenter is laying out a corner and needs to verify the diagonal length of legs measuring 5 inches and 12 inches.
- Step 1: Set leg a = 5, leg b = 12.
- Step 2: Square both legs: 5² = 25, 12² = 144.
- Step 3: Add squared values: 25 + 144 = 169.
- Step 4: Take the square root of 169 to find hypotenuse c = 13.
Frequently Asked Questions
What is a Pythagorean triple?
A Pythagorean triple consists of three positive integers (a, b, c) that satisfy the formula, such as (3, 4, 5), (5, 12, 13), or (8, 15, 17).
Which side of a right triangle is the hypotenuse?
The hypotenuse is always the longest side and is situated directly opposite the 90-degree right angle.
Can a hypotenuse be shorter than one of the legs?
No. Geometrically, the hypotenuse must always be strictly longer than either individual leg.