What this calculator does
The hypotenuse is the longest side of a right-angled triangle, always the one opposite the right angle. Given the two shorter sides, it comes directly from c = √(a² + b²).
This calculator does just that: enter the two legs and it returns the hypotenuse, with the triangle’s area shown alongside for good measure.
The formula
Square each of the two known legs, add the results together, then take the square root. That single calculation is the whole of it, since it is a direct application of c = √(a² + b²) with no further rearranging needed.
| Term | Meaning |
|---|---|
| a, b | The two legs of the right triangle, the sides that meet at the right angle. |
| c | The hypotenuse, the side opposite the right angle, always the longest of the three. |
The inputs explained
| Field | What to enter |
|---|---|
| Leg a | The length of one leg of the right triangle. |
| Leg b | The length of the other leg. |
When to use it
Finding a diagonal measurement
The diagonal across a rectangle, screen, doorway or plot of land, when only the two straight sides are known, is exactly the hypotenuse of the right triangle those sides form.
Working out cable, ladder or brace length
A support that runs diagonally between a known horizontal and vertical distance is a hypotenuse, so this gives the minimum length needed to span the gap.
Quick homework or exam checks
When the only thing needed is the hypotenuse from two known legs, this skips the fuller Pythagoras walkthrough and gives just that one number.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Hypotenuse for a fixed leg of 5, across a range of second legs
A fixed leg of 5, across a range of second-leg lengths.
Questions
What is the hypotenuse?
The longest side of a right-angled triangle, positioned opposite the right angle. It is always longer than either of the other two sides on its own.
How do you find the hypotenuse?
Square both of the other two sides, add them together, then take the square root: c = √(a² + b²). This only works for a right-angled triangle.
What is the hypotenuse formula?
c = √(a² + b²), where a and b are the two legs meeting at the right angle and c is the hypotenuse. It comes directly from Pythagoras theorem, a² + b² = c².
Can this calculator find a missing leg instead of the hypotenuse?
Not this one, since it is built specifically for the hypotenuse-from-two-legs direction. The Pythagoras theorem hypotenuse calculator covers both directions, including solving for a missing leg.
To solve the same theorem the other way round, for a missing leg, use the Pythagoras theorem hypotenuse calculator. For the midpoint or distance between two coordinate points instead, see the midpoint calculator.