Find the longest side
Hypotenuse Calculator
Enter the two legs of a right triangle and find the hypotenuse instantly, with the formula, the working, and a live diagram.
- Step-by-step working
- All units supported
- Works offline
- 100% free
Core calculator
Find the Hypotenuse from Two Legs
Result
Enter values to calculate the missing side or verify a triangle.
Show calculation steps
Recent calculations
Need to find a missing leg instead? Use the Missing Side Calculator.
Formula
The Hypotenuse Formula
c = √(a² + b²)
In a right triangle, the hypotenuse is the side opposite the 90-degree angle. To find it, square both legs, add the results, and take the square root. This relationship, known as the Pythagorean theorem, means the hypotenuse is always longer than either leg but shorter than the sum of both legs.
This page focuses on finding c. To solve for a missing leg, visit the Missing Side Calculator.
How it works
How to Calculate the Hypotenuse
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Enter leg a
Type the length of the first leg into the field labeled a. You can use any number, including decimals.
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Enter leg b
Type the length of the second leg into the field labeled b. If both legs are the same length, the triangle is an isosceles right triangle (45-45-90).
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Choose a unit and precision
Select meters, centimeters, feet, or inches from the unit dropdown. Adjust decimal places if you need more or less precision in the result.
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Read the hypotenuse
The value of c appears instantly. Click "Show calculation steps" to see the full working: the formula, the substitution, and the square root evaluated step by step.
The calculator uses the formula c = √(a² + b²) for every calculation. No
rounding happens until the final step, so intermediate values stay as precise as your browser's
floating-point arithmetic allows.
Examples
Hypotenuse Examples with Full Working
Click any example to load it into the calculator above.
3-4-5 triangle
The classic introductory example with an exact whole-number hypotenuse.
Basic
5-12-13 triangle
A clean benchmark for checking accuracy with another integer result.
Basic
Screen diagonal
Turn width and height into a diagonal measurement for a real-world display problem.
Intermediate
FAQ
Frequently Asked Questions
The hypotenuse is the longest side of a right triangle. It is always the side directly
opposite the 90-degree angle. In the Pythagorean theorem formula a² + b² = c²,
the variable c represents the hypotenuse. No matter how the triangle is oriented,
the hypotenuse is never one of the two sides that form the right angle.
Square each leg, add the two results, then take the square root of the sum. For example, if
a = 6 and b = 8, then
c = √(6² + 8²) = √(36 + 64) = √100 = 10. Enter those
values in the calculator above and it will show every step automatically.
Not with the Pythagorean theorem alone. You need two pieces of information. If you know one
leg and one angle, use trigonometry: c = a / sin(A) or c = b / cos(B).
The Triangle Solver on the Right Triangle Calculator page
handles those cases. This calculator requires both legs.
The hypotenuse formula is c = √(a² + b²), derived directly from the
Pythagorean theorem a² + b² = c². You square both legs, add them, and
take the square root. This formula only applies to right triangles, triangles with exactly one
90-degree angle.
Yes. In any right triangle, the hypotenuse is always longer than either leg. Since
c² = a² + b² and both squared legs are positive, c²
must be greater than either a² or b² alone, which means
c > a and c > b.
In a 45-45-90 triangle, both legs are equal. If each leg has length a, the
hypotenuse is a√2. For example, if both legs are 5, the hypotenuse is
5√2 ≈ 7.071. Enter a = 5 and b = 5 in the
calculator to confirm.