Pythagorean Theorem Calculator
Calculate the hypotenuse of a right triangle using the Pythagorean theorem (a² + b² = c²).
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How to use this tool
- Enter side a and side b in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your hypotenuse c and the full breakdown beneath it.
Find the hypotenuse of a right triangle: c = √(a² + b²).
Formula
c = √(a² + b²)
Where a and b are the two legs of a right triangle and c is the hypotenuse (the side opposite the right angle).
How it works
The calculator squares both leg lengths, adds the squares, and takes the square root to find the hypotenuse, directly applying the Pythagorean theorem. The result is in the same unit as the inputs and assumes the triangle contains a perfect 90-degree angle.
Worked example
Worked example: legs 3 and 4
- Inputs: a = 3, b = 4.
- Square each leg: 3² = 9, 4² = 16.
- Sum: 9 + 16 = 25.
- Hypotenuse: c = √25 = 5.
c = 5
Common mistakes to avoid
- Using the formula on non-right triangles where it does not apply; always verify a right angle exists first.
- Confusing which side is the hypotenuse: c must be the longest side opposite the right angle.
- Computing a + b = c instead of a² + b² = c², a common shortcut error when estimating mentally.
Key terms
- Hypotenuse
- The longest side of a right triangle, located opposite the right angle; calculated as √(a² + b²).
- Leg
- Either of the two shorter sides of a right triangle that form the right angle.
- Pythagorean triple
- A set of three positive integers a, b, c satisfying a² + b² = c²; the classic example is 3, 4, 5.
- Right angle
- An angle of exactly 90 degrees; defines the corner between the two legs of a right triangle.
- Pythagorean theorem
- The fundamental relationship a² + b² = c² holding for any right triangle with legs a, b and hypotenuse c.
Frequently asked questions
- What is the Pythagorean theorem?
- For a right triangle with legs a and b, the hypotenuse c satisfies a² + b² = c². Classic example: 3² + 4² = 9 + 16 = 25 = 5².