Pythagorean Theorem Calculator
Solve a right triangle's missing side from the other two: c = √(a² + b²) or a = √(c² − b²). Leave one side empty to solve for it. How it works
Use the Pythagorean Theorem Calculator
About the Pythagorean Theorem Calculator
A right triangle with legs 3 and 4 has a hypotenuse of 5: c = √(3² + 4²) = √25. Fill in two sides, leave the third empty, and the calculator solves it as c = √(a² + b²) or, for a leg, a = √(c² − b²), to 10 significant figures.
Solving for the missing side
| Side a | Side b | Side c | Solved |
|---|---|---|---|
| 3 | 4 | empty | c = 5 |
| 5 | 12 | empty | c = 13 |
| 6 | 8 | empty | c = 10 |
| 1 | 1 | empty | c = 1.414213562 |
| 2 | 3 | empty | c = 3.605551275 |
| empty | 12 | 13 | a = 5 |
| 8 | empty | 17 | b = 15 |
| 1920 | 1080 | empty | c = 2202.90717 |
As the tool shows them, to 10 significant figures. The last row is the diagonal of a 1920 by 1080 rectangle.
How to use this tool
- Enter two of the three sides: side a and side b are the legs, side c is the hypotenuse.
- Leave the side you want empty. The result updates as you type, says which side it solved and shows the working, such as c = √(3² + 4²) = 5.
- Use the same unit for every side. The answer is in that unit.
Frequently asked questions
- How do I find the hypotenuse of a right triangle?
- Square both legs, add them and take the square root. For legs 3 and 4, 9 + 16 = 25 and the square root is 5. Enter 3 and 4 and leave side c empty to see c = 5.
- How do I find a missing leg?
- Subtract the square of the known leg from the square of the hypotenuse and take the root. With c = 17 and a = 8 the other leg is 15. If c is shorter than the leg you entered, the tool says the hypotenuse must be at least as long.
- What is the 3-4-5 rule?
- A triangle with sides 3, 4 and 5 has a right angle, and so does any multiple of it, such as 6-8-10 (enter 6 and 8 to get 10) or 5-12-13. Carpenters mark 3 units along one edge and 4 along the other: if the diagonal between the marks is 5, the corner is square, to within the accuracy of the measuring.
- How do I find the diagonal of a rectangle or a screen?
- The diagonal is the hypotenuse of a right triangle whose legs are the width and the height. A 1920 by 1080 rectangle has a diagonal of 2202.90717, and a 3 by 4 rectangle has 5.
- Why does it say all three sides are entered?
- The tool solves for one empty side. With all three filled in there is nothing to solve, so clear the one you want. With two or more empty it asks you to enter two sides.
- Can it find the angles of the triangle?
- No, it returns the missing side only. The right triangle calculator takes the same two sides and also gives both acute angles, the area and the perimeter: legs 3 and 4 give angles of 36.8699° and 53.1301°.
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