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Pythagorean Theorem Calculator
The missing side of a right-angled triangle, from the other two sides.
Missing side
How it works
Hypotenuse: c = √(a² + b²) A leg: b = √(c² − a²), where c is the hypotenuse and must be the longest side Area = (leg 1 × leg 2) ÷ 2
Worked example: legs of 3 and 4 give a hypotenuse of √(3² + 4²) = √25 = 5, and the area is (3 × 4) ÷ 2 = 6. In the other direction, a hypotenuse of 5 and a leg of 3 give the other leg as √(25 − 9) = √16 = 4.
Frequently asked questions
Which side is the hypotenuse?
The side opposite the right angle, and always the longest side. In the “find a leg” mode, enter the hypotenuse as Side 2 — it must be longer than Side 1, or the triangle cannot exist.
What if I get a negative number under the square root?
That means the claimed hypotenuse is shorter than the leg, which no right-angled triangle allows. The calculator shows a dash and a note instead of an imaginary number.
Does this work for any triangle?
No — only right-angled triangles, where one angle is exactly 90 degrees. For other triangles, use the base-and-height or three-sides area method instead.
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