Pythagorean Theorem Calculator (Solve Any Side)

Our Pythagorean theorem calculator turns two side measurements into the missing third side of a right triangle and verifies whether three given sides actually form a right triangle. The core relationship a² + b² = c² is simple, but real-world measurements are noisy. This page gives instant, hydration-safe results and explains each step so you can trust the numbers in the shop, on site, or in class.

The hypotenuse c is always the longest side because it’s opposite the right angle. If a supposed hypotenuse is not longer than each leg, the triangle cannot be right-angled. That check is built into the solver; if you supply all three sides, it reports PASS/FAIL and a residual that quantifies how far the numbers are from the ideal identity. A small residual indicates measurement rounding; a large one means the triangle isn’t right.

In practical work, you’ll use this calculator for layout (marking square corners), estimating ladder reach, locating anchors, placing screens, and checking rectangular structures. In math class, it’s handy for homework and test prep: the tool shows the exact algebraic step used (for example, c = √(a² + b²)) and the numeric substitution with your inputs, so you can mirror the reasoning on paper.

Keep units consistent. If you enter a and b in inches, c will be in inches too. If you switch to centimeters or meters, the geometry doesn’t change—only the unit label does. For construction tolerances, round up materials slightly to account for saw kerf and fastener placement. For coursework, show units and round only at the final step.

The theorem extends to scaled and similar triangles: doubling both legs doubles the hypotenuse. It also underpins coordinate distance (the Euclidean norm) and appears in trigonometry, vectors, physics, and analytics. Mastering it builds intuition for length, distance, and error—skills that transfer to many fields.