Enter two sides of a right triangle to find the third, with steps, exact radicals and a labelled diagram. Runs on your device.
The Pythagorean theorem says that in a right triangle the squares of the two legs add up to the square of the hypotenuse, a² + b² = c², so any two sides give the third. The page opens with a = 3 and b = 4 and leaves c empty, so c is the side it solves: c² = 3² + 4² = 9 + 16 = 25, and c = √25 = 5. Leave exactly one box empty and that is the side the page finds. The legs a and b are the two sides that meet at the right angle, and the hypotenuse c is the long side across from it. The working box repeats each line with your own numbers.
To find a leg, subtract: a² = c² − b². With c = 13 and b = 12, a² = 169 − 144 = 25 and a = 5. The hypotenuse is always the longest side, so if c is not longer than the leg you typed, the page shows a message under the c box and no result, because no right triangle has those sides. Sides must be more than 0 and at most 1,000,000,000. Decimals work, for example legs of 1.5 and 2 give a hypotenuse of 2.5. Use the same unit for every side; the answer comes out in that unit.
When the sides are whole numbers and the answer is not, the page also shows the exact value. With a = 5 and b = 5, c² = 50, and 50 = 25 × 2 contains the square 25, so c = √50 = 5√2, which is about 7.0711. The page takes the largest square factor out of the number under the root. Exact forms are shown for whole-number sides only, up to the size a computer stores without rounding. Decimal places are your choice from 0 to 10, and decimals are rounded only when shown.
Fill in all three boxes and the page checks instead of solving: 5, 12 and 13 pass because 25 + 144 = 169, while 5, 6 and 7 do not because 25 + 36 = 61 and not 49. Whole-number sets that pass, such as 3-4-5, 5-12-13, 8-15-17 and 7-24-25, are called Pythagorean triples, and the page says when you have one. For a solved triangle you also get the area, a × b ÷ 2, the perimeter, and the two acute angles from A = tan⁻¹(a ÷ b). The page works for right triangles only; for any other triangle use the triangle calculator, which uses the laws of sines and cosines.
Square both legs, add them and take the square root: c = √(a² + b²). For legs of 6 and 8, c² = 36 + 64 = 100, so the hypotenuse is 10. Type a and b and leave c empty.
Subtract the squares: a = √(c² − b²). With a hypotenuse of 17 and a leg of 15, a² = 289 − 225 = 64, so the other leg is 8. Type b and c and leave a empty. The hypotenuse must be the longer number.
5√2. The number 50 is 25 × 2, and 25 is the square of 5, so √50 = 5√2, about 7.0711. Enter two legs of 5 and 5 and the page shows this exact form beside the decimal.
Fill in all three boxes. The page tests a² + b² = c² with c as the hypotenuse. For 7, 24 and 25 it finds 49 + 576 = 625 and says yes. For 5, 6 and 7 it finds 61 against 49 and says no.
The hypotenuse is the longest side of a right triangle, because c² = a² + b² is bigger than either square alone. If you type c = 4 and b = 5, no triangle exists, so the page asks for a longer c instead of showing a result.
No. The numbers are processed in your browser and are not uploaded. They are not stored on your device either, and reloading the page puts the 3 and 4 example back.