Hypotenuse Calculator (a² + b² = c²)
Solve a² + b² = c² step by step: find the hypotenuse from two legs, find a missing leg, or test whether three sides form a right triangle — with exact simplified radicals like 5√2, a scaled diagram, area and perimeter.
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About this tool
This page opens the Pythagorean theorem calculator in hypotenuse mode: enter the two legs of a right triangle and c = √(a² + b²) is computed with every substitution shown. The classic 3 and 4 give 9 + 16 = 25 and c = √25 = 5; legs of 5 and 5 give the irrational √50, which the calculator simplifies to the exact 5√2 before showing ≈ 7.0711.
Decimals are handled exactly by scaling to whole numbers first, so 1.5 and 2 produce precisely 2.5. Together with the missing side you get the area and perimeter of the triangle and a diagram drawn to your proportions with the right angle marked — a complete picture, not just one number.
The hypotenuse question appears anywhere a right angle does: the diagonal of a rectangle or screen, the length of a ladder against a wall, a roof slope from run and rise, the straight-line distance between two points on a grid. If the angle between your two known sides is not 90°, use the general triangle calculator on this site instead — the law of cosines handles any angle.
Example. Legs 3 and 4 in hypotenuse mode return c equal to 5, because 9 plus 16 equals 25.
Limit. The check mode only tests whether three lengths satisfy a squared plus b squared equals c squared, and it does not solve a non-right triangle.