First confirm the right angle
The Pythagorean theorem applies to a triangle with one 90-degree angle. The hypotenuse lies opposite that angle and is always the longest side. It is represented by c in the standard formula.
For a non-right triangle, adding the squares of two sides does not generally give the square of the third. Do not assume a sketch is drawn accurately enough to prove an angle.
Choose addition or subtraction
If both legs are known, add their squares and take the positive square root to find the hypotenuse. If one leg and the hypotenuse are known, subtract the known leg’s square from the hypotenuse’s square.
Lengths use the positive root. A negative radicand in a missing-leg problem usually means the sides were mislabeled or the supplied lengths are inconsistent.
Keep units and rounding consistent
Convert both known lengths to one unit before squaring. Retain exact squares and use the calculator only for the final root when possible.
The Root calculator can evaluate the final square root; it does not validate an entire triangle for you. The scientific calculator can handle a complete arithmetic expression such as sqrt(5^2+12^2).
LET’S WORK IT THROUGH
A right triangle has legs 5 and 12. Find the hypotenuse.
- 5² + 12² = 25 + 144 = 169.
- c = √169.
- Take the positive length: c = 13.
THE ANSWERThe hypotenuse is 13 units.
YOUR TURN
A small check for understanding.
A hypotenuse is 10 and one leg is 6. Find the other leg.
Reveal the answer
8 units. √(10² − 6²) = √64 = 8.
Now try your own numbers.
The root calculator includes input guidance and the limits of its supported calculations. Use it alongside the method above.
Open Root calculator ↗A note on precision: preserve exact fractions where possible and round numerical results at the end. Found an unclear step? Prepare a correction report.