Pythagorean Theorem Calculator — Solve for Any Side

Fill in exactly two of the three sides, and leave the one you want to solve for blank.

Leg A

Leg B

Hypotenuse C

Result

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How to Use This Tool

Enter any two of the three sides.
Leave the side you want to solve for blank.
Click Solve for the missing side.

The Pythagorean Theorem

a² + b² = c²

Where a and b are the two legs of a right triangle, and c is the hypotenuse (the side opposite the right angle, always the longest side).

Solving for Each Variable

Hypotenuse: c = √(a² + b²)
Leg A: a = √(c² − b²)
Leg B: b = √(c² − a²)

Real-World Applications

Construction: checking if a corner is truly square (the classic 3-4-5 triangle method)
Finding the diagonal distance across a rectangular space
Navigation and physics problems involving perpendicular distances

Frequently Asked Questions

Why must the hypotenuse be the longest side?

The hypotenuse is defined as the side opposite the right angle in a right triangle, and geometrically, this side is always the longest of the three — if your "hypotenuse" value is shorter than a leg, the inputs are inconsistent with a valid right triangle.

What is the 3-4-5 triangle method used in construction?

It's a practical application of the Pythagorean theorem (3² + 4² = 5²) that builders use to verify a corner is exactly 90 degrees by measuring 3 units down one side, 4 units down the other, and checking the diagonal measures exactly 5 units.

This calculator is provided for general informational and estimation purposes only. Results should not be treated as professional financial, tax, legal, medical, or engineering advice. Always verify critical calculations with a qualified professional or official source before making decisions.