Pythagorean Theorem Calculator
Fill in any two sides and leave the third blank.
Example
With legs a = 3 and b = 4, c = √(3² + 4²) = √25 = 5. The area is 3 × 4 / 2 = 6 and the perimeter is 3 + 4 + 5 = 12.
The Pythagorean theorem
In a right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c². The hypotenuse c is always the longest side.
How to use this calculator
Enter any two of the three sides and leave the third blank. Leave c blank to find the hypotenuse, or leave a or b blank to find a leg. The calculator also gives the area, the perimeter and the two acute angles.
Worked examples
- Find the hypotenuse: legs 6 and 8 give c = √(36 + 64) = √100 = 10.
- Find a leg: hypotenuse 13 and leg 5 give b = √(169 - 25) = √144 = 12.
Common Pythagorean triples
Sets of whole numbers that satisfy the theorem are called Pythagorean triples. The most common are 3-4-5, 5-12-13, 8-15-17 and 7-24-25. Any multiple of a triple also works, so 6-8-10 and 9-12-15 are right triangles too.
Where it is used
- Checking that a corner is square in construction, using the 3-4-5 method.
- Finding the straight-line distance between two points, which is the distance formula.
- Finding the diagonal of a rectangle or how far up a wall a ladder reaches.
Mistakes to avoid
- Using the theorem on a triangle that is not a right triangle.
- Adding the squares when you should subtract, which happens when you solve for a leg.
- Forgetting to take the square root at the end.
For the slope and distance between two points on a graph, use the slope calculator.