How To Use The Pythagorean Theorem Calculator
For right triangles, the squares of the two shorter sides add exactly to the square of the longest. That single relation turns any two known sides into the third.
Hypotenuse from legs a and b
5
- Missing leg from leg a and the hypotenuse
- 4
- Area of the triangle
- 6
- Perimeter of the triangle
- 12
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
c^2 = a^2 + b^2, so c = sqrt(a^2 + b^2)
- a, b
- The two legs meeting at the right angle
- c
- Hypotenuse — the side opposite the right angle, and always the longest
- a^2 + b^2
- Squared lengths whose sum equals the squared hypotenuse
How to check the result by hand
- 1
Confirm there is a right angle
The theorem applies only to right triangles. If the known sides do not meet at ninety degrees, stop and use the law of cosines instead.
- 2
Put both known lengths in the same unit
Convert before squaring. Summing squares of measurements in different units produces a number with no physical meaning.
- 3
Identify whether you are missing the hypotenuse or a leg
Missing the longest side means add the squares; missing a shorter side means subtract. Getting this backwards is the single most frequent error.
- 4
Compute and take the square root
Here 3^2 + 4^2 = 9 + 16 = 25, so the hypotenuse is 5. The square root returns you to the original unit rather than squared units.
- 5
Sanity-check against the longest known side
A computed hypotenuse must exceed both legs; a computed leg must be shorter than the hypotenuse. If not, you added where you should have subtracted.
For worked examples, common mistakes and the limits of this formula, read the full How To Use The Pythagorean Theorem page.