Find a missing side of a right triangle: a² + b² = c².
In a right triangle a² + b² = c². With legs 3 and 4, c = √25 = 5 — the famous 3-4-5 triangle.
The Pythagorean theorem says that in a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides. Leave one box empty and this calculator finds the missing side with the working shown and flags Pythagorean triples; the second tool checks whether any three sides form a right, acute or obtuse triangle.
For angles and area use the Right Triangle Calculator; for non-right triangles the Triangle Calculator. The distance between two points is the same theorem — see the Distance Calculator — and the Root Calculator simplifies the square roots.
The calculator applies the standard method step by step.
| Item | Value |
|---|---|
| a | 3 |
| b | 4 |
| c | 5 |
| Area | 6 |
| Perimeter | 12 |
| Angle A | 36.86989765° |
| Angle B | 53.13010235° |
| Working |
|---|
| c² = a² + b² = 9 + 16 = 25 |
| c = √25 = 5 |
| Legs | Hypotenuse |
|---|---|
| Legs 3 and 4 | 5 |
| Legs 5 and 12 | 13 |
| Legs 8 and 15 | 17 |
| Legs 1 and 1 | 1.41421356237 |
| Legs 7 and 24 | 25 |
| a | b | c | Check a² + b² = c² |
|---|---|---|---|
| 3 | 4 | 5 | 9 + 16 = 25 |
| 5 | 12 | 13 | 25 + 144 = 169 |
| 8 | 15 | 17 | 64 + 225 = 289 |
| 7 | 24 | 25 | 49 + 576 = 625 |
| 20 | 21 | 29 | 400 + 441 = 841 |
| 9 | 40 | 41 | 81 + 1600 = 1681 |
| 6 | 8 | 10 | 36 + 64 = 100 |
| 12 | 16 | 20 | 144 + 256 = 400 |
| 15 | 20 | 25 | 225 + 400 = 625 |
| 10 | 24 | 26 | 100 + 576 = 676 |
In a right triangle, a² + b² = c², where c is the hypotenuse.
Square both legs, add them and take the square root: legs 3 and 4 give √25 = 5.
Subtract the square of the known leg from the square of the hypotenuse and take the square root.
Three whole numbers that satisfy a² + b² = c², such as 3-4-5, 5-12-13 and 8-15-17.
Only for right triangles. For others use the law of cosines.
It is named after the Greek mathematician Pythagoras, but it was known to Babylonian and Indian mathematicians (Baudhayana) earlier.
It uses the standard method: a² + b² = c² c = √(a² + b²) a = √(c² − b²) The full working and a worked example are shown on this page.
Decimal results use standard double-precision arithmetic (about 15–16 significant digits). Tools that work with whole numbers — big numbers, factors, bases, combinations — use exact integer arithmetic, so no digits are lost.
Yes for checking your work and learning the method. The steps and formula are shown so you can understand the answer, but follow your teacher's rules about calculators in exams.
No. Everything is calculated in your browser and nothing you enter is uploaded or saved.
