Pythagorean Theorem Calculator

Find the missing side of a right triangle using the Pythagorean theorem. Calculate area, perimeter, and angles.

This calculator solves the two classic Pythagorean theorem problems from a single pair of inputs, switching formulas entirely based on which mode you select. In hypotenuse mode, Side A and Side B are treated as the two legs of a right triangle, and the calculator finds the hypotenuse via the square root of the sum of their squares. In missing-side mode, the roles change completely: Side A becomes the hypotenuse itself and Side B becomes one known leg, and the calculator solves algebraically for the other leg instead. Of the two number fields, Side B has noticeably more pull over the reported hypotenuse than Side A does at the calculator's default values — nudging Side B by ten percent moves the hypotenuse by roughly 1.8 times the proportional amount that the same ten percent nudge to Side A does, because Side B (4) makes up a larger share of the resulting hypotenuse (5) than Side A (3) does, and a leg's influence on the hypotenuse scales with how large a fraction of the hypotenuse it already represents. Both legs push the result in the same direction: growing either one always grows the hypotenuse, never shrinks it. The two angle readouts also switch which inverse trig function computes them depending on mode — arctangent of a ratio of the two legs in hypotenuse mode, arcsine of a ratio against the hypotenuse in missing-side mode — rather than using one formula throughout. A gap worth flagging: in missing-side mode, if the leg you enter for Side B is actually longer than the hypotenuse you entered for Side A, the calculator does not flag the geometric impossibility — it clamps the negative quantity under the square root to zero and reports a missing side of exactly 0 instead of an error.