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The Pythagorean Theorem
a² + b² = c²
where c is the hypotenuse (longest side, opposite the right angle)
c = √(a² + b²)
Find the hypotenuse
a = √(c² − b²)
Find leg a
b = √(c² − a²)
Find leg b
The Pythagorean theorem calculator lets you solve for any missing side of a right triangle using the formula a² + b² = c². Whether you need to find the hypotenuse or one of the two legs, simply enter the two known values and get an instant answer — complete with step-by-step working, all three angles, area, and perimeter. No algebra required.
The Pythagorean theorem states that in any right triangle, the square of the hypotenuse (c) equals the sum of the squares of the two legs: a² + b² = c². It is named after the ancient Greek mathematician Pythagoras and is one of the most fundamental relationships in geometry.
To find the hypotenuse c, enter the lengths of both legs (a and b) and select 'Solve for c'. The calculator computes c = √(a² + b²). For example, legs of 3 and 4 give a hypotenuse of 5 (the classic 3-4-5 Pythagorean triple).
Yes. Select 'Solve for a' or 'Solve for b', then enter the other leg and the hypotenuse. The formula rearranges to a = √(c² − b²) or b = √(c² − a²). The hypotenuse must always be larger than either leg for a valid triangle.
Pythagorean triples are sets of three positive integers that satisfy a² + b² = c² exactly. Common examples include 3-4-5, 5-12-13, 8-15-17, and 7-24-25. Any multiple of a triple (e.g. 6-8-10) is also a valid Pythagorean triple.