THE NUMORIX GUIDE
How to use the Pythagorean Theorem Calculator
Last reviewed September 14, 2026
What this calculator does
For the two perpendicular legs a and b of a right triangle, calculate the hypotenuse c = sqrt(a^2+b^2).
Formula and method
For the two perpendicular legs a and b of a right triangle, calculate the hypotenuse c = sqrt(a^2+b^2).
Variables and inputs
Side a defaults to 3 and side b to 4. Both are positive lengths in the same unit; the result c is the hypotenuse.
Worked example
For a=3 and b=4: c = sqrt(3^2+4^2) = sqrt(9+16) = sqrt(25) = 5.
How to interpret the result
The theorem applies only to right triangles and relates the two legs to the side opposite the right angle.
Common mistakes to avoid
Do not use the theorem on an oblique triangle, and do not forget to take the square root after adding the squared legs.
Assumptions and limitations
The UI only solves for c from two legs; it does not solve for a missing leg when the hypotenuse is supplied or validate a complete triangle.
Practical use and checks
The Pythagorean Theorem Calculator solves for the hypotenuse of a right triangle from its two perpendicular legs. Enter a = 3 and b = 4 as a check; the result should be c = 5 because the square root of 9 plus 16 is 5. The supplied sides must meet at the right angle, and c should be the longest side. A diagonal across a rectangular panel is a practical example: measure the two side lengths in the same unit before calculating. Use the result for a right-angle layout, cable length estimate, or geometry check, but do not apply the theorem to an oblique triangle. If the hypotenuse and one leg are known, rearrange the equation or use a tool that supports that mode rather than placing the hypotenuse in a leg field. Units are squared during the calculation and return to a linear unit after the square root, so meters and feet cannot be mixed. The calculator assumes flat Euclidean geometry, exact right angles, and positive lengths; it does not include measurement tolerance, sagging cable, wall thickness, or a three-dimensional offset. For a construction cut, add the appropriate allowance only after the geometric diagonal has been verified.