Pythagorean theorem calculator
Work out the hypotenuse from two legs, or the missing leg when you know the hypotenuse and one side.
With legs of 3 and 4 the hypotenuse is 5.0000.
Formula
a and b are the legs and c the hypotenuse — the longest side, opposite the right angle.
How we got there
The theorem holds only in a right-angled triangle. The hypotenuse is always longer than either leg.
How to use Pythagoras by hand
- Square both known sides
For 3 and 4: 3² = 9 and 4² = 16.
- Add the squares if you want the hypotenuse
9 + 16 = 25.
- Take the square root
√25 = 5. That is the hypotenuse.
- For a leg, subtract instead of adding
b = √(c² − a²). For c = 5 and a = 3: √(25 − 9) = √16 = 4.
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Frequently asked questions
Add the squares of the legs and take the square root: c = √(a² + b²). For 3 and 4 the answer is 5.
Subtract the square of the known leg from the square of the hypotenuse and take the square root.
Three whole numbers that satisfy the theorem, such as 3, 4, 5 or 5, 12, 13.
When finding a leg, the hypotenuse must be the longest side. Enter a smaller value and no such triangle exists.
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