Pythagorean Theorem Calculator
In any right triangle the squares of the two legs add up to the square of the hypotenuse. Enter two sides to find the third: the hypotenuse from both legs, or a missing leg from the hypotenuse and the other leg.
- Area of the triangle
- 6 ft²
- Perimeter
- 12 ft
Saved setups
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Your recent calculations
Results you calculate here are kept on this device so you can come back to them.
Formula
How to use it
- Choose whether you are solving for the hypotenuse or a leg.
- Enter the two sides you know, each in its own unit.
- Read the missing side, plus the triangle’s area and perimeter.
Worked examples
Legs of 3 ft and 4 ft: hypotenuse 5 ft, which is 1.524 m
- Missing side
- 5 ft
- Area of the triangle
- 6 ft²
- Perimeter
- 12 ft
A leg of 5 m and a hypotenuse of 13 m
- Missing side
- 12 m
- Area of the triangle
- 30 m²
- Perimeter
- 30 m
A 9 ft leg under a 15 ft hypotenuse: the other leg is 12 ft (3.6576 m)
- Missing side
- 12 ft
Pythagorean triples
Some right triangles have whole-number sides: 3-4-5, 5-12-13, 8-15-17 and 7-24-25 are the most common, along with any multiple of them such as 6-8-10 or 9-12-15.
Squaring a corner with 3-4-5
Builders check a right angle by measuring 3 feet along one side and 4 feet along the other; if the diagonal between those marks is exactly 5 feet, the corner is square. For a bigger layout, scale it up: a 12 ft by 16 ft deck is square when its diagonal measures 20 ft.
Questions people ask
What is the hypotenuse if the legs are 3 and 4?
5, because 3² + 4² = 9 + 16 = 25 and √25 = 5.
How do I find a missing leg?
Subtract the square of the known leg from the square of the hypotenuse and take the square root. With a hypotenuse of 13 and a leg of 5: √(169 − 25) = 12.
Does the Pythagorean theorem work for every triangle?
No, only for right triangles. For other triangles use the law of cosines, which reduces to the Pythagorean theorem when the angle is 90°.