Updated · Built and checked by the PlinzoTools team, formulas tested against published sources
Calculate a right triangle's hypotenuse from its two legs.
10.0000
This tool calculates the hypotenuse of a right triangle -- the direct, single-purpose form of the Pythagorean theorem.
Enter both legs. The hypotenuse appears instantly.
c = √(a² + b²)
This calculator takes the two legs of a right triangle, the sides that meet at the 90 degree corner, and returns the length of the longest side opposite that corner. Both legs must be numbers greater than zero; if either is zero, negative or blank, the result area asks you to enter both legs instead of displaying a value. The answer is shown to four decimal places. The tool is deliberately narrow: it does not return the angles, the area or the perimeter, and it does not solve for a missing leg.
Whole-number triples make it easy to check that the tool agrees with your own work. Legs of 5 and 12 give a square root of 169, so the hypotenuse is exactly 13. Legs of 3 and 4 give 5. Real measurements rarely come out so neatly. With legs of 2.5 and 6, the sum of squares is 6.25 + 36 = 42.25, and the square root is 6.5. Two equal legs of 1 give the square root of 2, which is 1.4142, the well-known diagonal of a unit square. That last case is the reason a diagonal is always about 41 percent longer than a side of a square.
A practical scenario: a rectangular garden bed is 12 feet by 9 feet and you want to check that it is square by comparing diagonals. If the corners are true right angles, the diagonal should be 15 feet, since 144 + 81 = 225. If your tape measures 15.4 feet, the bed is skewed and needs adjusting. Carpenters use the same 3-4-5 idea, scaled up, when laying out foundations and decks.
You can extend the tool to three dimensions by using it twice. For a box that is 3 by 4 by 12 units, first find the floor diagonal from the legs 3 and 4, which is 5. Then treat that 5 as one leg and the height 12 as the other: the square root of 25 + 144 is 13. This gives the longest straight line that fits inside the box, useful for checking whether a rod, pipe or rolled poster will fit into a carton.
The most frequent error is entering the hypotenuse as one of the legs. If you already know the long side and one leg, this tool will produce a value larger than the number you entered, which is a signal to use a tool that solves for a missing leg instead. Another mistake is mixing units, such as one leg in inches and the other in feet. Convert both to the same unit first; the result comes back in that unit. Finally, remember that the theorem applies only to right triangles. If the corner is not exactly 90 degrees, the Law of Cosines is the correct generalisation.
Because the display rounds to four decimals, a hand calculation using a rounded square root may differ slightly in the final digit. For construction or fabrication, the real limit is measurement accuracy: a tape reading that is off by an eighth of an inch on each leg changes the computed diagonal by a comparable amount. Treat the result as a design value, then confirm the finished piece with a physical measurement before cutting expensive material. The tool is also helpful for non-physical uses, such as finding the straight-line distance between two points on a grid when you know the horizontal and vertical differences, or the on-screen length of a diagonal movement in game and graphics work.
Use the Pythagorean Theorem Calculator, which solves for any of the three sides.
Only if the other leg is zero, which is not a real triangle and is rejected by the tool. For any valid inputs the hypotenuse is strictly longer than each leg.
No. Squaring and adding are order-independent, so swapping leg a and leg b gives exactly the same hypotenuse.
Subtract the x values to get the horizontal difference and the y values for the vertical difference. Enter the absolute sizes of those two differences as the legs, and the result is the straight-line distance.
Most pairs of whole numbers do not produce a perfect square sum, so the square root is an irrational number. Only special sets such as 3-4-5 or 5-12-13 give whole results.
Reference: NIST Weights and Measures