Calculate the missing side of a right triangle from two known sides with visual diagram.
This calculator solves the right triangle relation a² + b² = c²: enter any two side lengths, and it returns the third, with a visual diagram of the labeled triangle. The catch most people hit: the hypotenuse is the side opposite the right angle and has to be identified as such, and when that side is missing you add the squares, but when a leg is missing you subtract them. The result is only valid for a triangle with one exact 90-degree angle; for anything else, the law of cosines, not this tool, gives the missing side.
A concrete input and expected output from the current implementation.
Input
Leg a = 5, hypotenuse c = 13; find leg b
Expected output
b = 12
With c as the hypotenuse, b² = c² - a² = 169 - 25 = 144, and the square root of 144 is 12. The three sides form the classic 5-12-13 Pythagorean triple, so every value comes out as an exact integer.
You enter two of the three sides, and the tool must know which one is the hypotenuse, the longest side and the one opposite the right angle. That choice fixes the operation: with the hypotenuse missing, it adds the squared legs and takes the root, sqrt(a² + b²); with a leg missing, it subtracts, sqrt(c² - b²). Mislabeling which side is the hypotenuse is the difference between these two computations.
The page draws a right triangle with the right-angle marker, labels the two known sides, and calls out the unknown one. The arithmetic is only possible when the inputs are geometrically consistent: both known sides positive, and a stated hypotenuse strictly longer than each stated leg. Otherwise the square-root step has no real result and no length exists to report.
Only right triangles, and the diagram always shows the 90-degree marker so you can confirm the input qualifies. With three sides and no known angle, a missing length is not determined by the Pythagorean relation. The general formula is the law of cosines, c² = a² + b² - 2ab cos(C), which also needs the included angle.
Because the missing value is a leg, and the relation rearranges to a² = c² - b²: you subtract the squared leg from the squared hypotenuse. The hypotenuse is the longest side, so every leg must be shorter than it. Adding would produce a length longer than the hypotenuse, which cannot be a side of the same triangle.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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