Hypotenuse Calculator
Find the longest side of a right triangle instantly using the Pythagorean theorem.
Hypotenuse
A²
--
B²
--
A² + B²
--
Common Hypotenuse Examples
a = 3, b = 4
Hypotenuse
5
(Right triangle)
a = 5.5, b = 7.2
Hypotenuse
9.06
(Rounded to 2 decimals)
a = 8, b = 15
Hypotenuse
17
(Pythagorean triple)
How to Use
- Enter Side A: Type the length of the first leg of the right triangle.
- Enter Side B: Add the second leg. Both values must be positive numbers.
- Select Unit and Precision: Choose a unit if you want one shown with the result, then set how many decimal places to display.
- Calculate: Click the button to instantly compute the hypotenuse using the Pythagorean theorem.
Formula Used
Calculate the hypotenuse by applying the Pythagorean theorem: c = √(a² + b²), where a and b are the triangle's legs. For example, if a = 3 and b = 4, then c = 5. This formula works for all right triangles with a 90° angle.
c = sqrt(a^2 + b^2)
Here, c is the hypotenuse, while a and b are the two shorter sides.
Why the Hypotenuse Matters
The hypotenuse is the longest side of a right triangle, and it sits directly opposite the right angle. It appears everywhere in geometry, construction, engineering, navigation, and physics because it helps describe diagonal distance.
Builders use it to check whether corners are square. Students use it in geometry problems. Designers and engineers rely on it for layout, slope, and structural calculations. Whenever you know the two perpendicular sides of a right triangle, the Pythagorean theorem gives you a fast and reliable way to find the missing diagonal.
Quick Tip:
If your triangle sides are 3 and 4, the hypotenuse is 5. This famous 3-4-5 triangle is often used in construction to verify perfect right angles.
Credible Source:
For a reliable explanation of the theorem behind this calculator, see Britannica: Pythagorean theorem.
Frequently Asked Questions
What is a hypotenuse in geometry?
In geometry, the hypotenuse is the side opposite the 90-degree angle in a right triangle. It is always the longest side, which means its side length is greater than the other two legs.
What equation does the hypotenuse formula use?
The equation is based on the Pythagorean theorem. You square each leg of the right triangle, add those values together, and then take the square root of the total. In formula form, that is c = sqrt(a^2 + b^2), which gives the final result for the missing side.
Can I enter decimal input values?
Yes. This calculator accepts whole numbers and decimals as input, so it works well for precise measurement tasks in real-world problems. The output can then be shown with the decimal precision you choose.
Do both side lengths need the same unit?
Yes. Side A and Side B should use the same unit before you calculate, because the result will be shown in that same unit. If your values start in different units, do a quick conversion first so the side length measurement stays accurate.
Can this solver handle non-right triangles?
No. This solver is specifically for right triangles, where the Pythagorean theorem applies directly. For any triangle that does not include a 90-degree angle, you would need a different formula.
Why is the hypotenuse always the longest side?
In any triangle, the longest side is opposite the largest angle. In a right triangle, the largest angle is the 90° angle, so the side opposite it, the hypotenuse, must have the greatest side length.
Can I use this for ramps, ladders, or diagonal distances?
Yes. If your setup forms a right triangle, this calculator is useful for finding a ramp length, ladder reach, screen diagonal, roof slope distance, or any other straight-line diagonal measurement. It is a practical way to turn two known side values into a clear output for real projects.