Pythagorean Theorem Calculator

1. Select what to solve for. Choose the hypotenuse (c) if you know both legs. Choose leg a or leg b if you know one leg and the hypotenuse. The unknown field grays out automatically.
2. Enter the two known sides. All values must be in the same unit (feet, meters, inches, etc.). The calculator applies the formula and shows a step-by-step solution.
3. Verify it is a right triangle. The Pythagorean theorem only works for right triangles (one 90-degree angle). If you have an oblique triangle, you need the law of cosines instead.

Practical example: a ramp rises 4 feet vertically over a horizontal distance of 10 feet. The ramp length = √(4² + 10²) = √(16 + 100) = √116 = 10.77 feet. The reference table below lists common Pythagorean triples where all three sides are whole numbers.

a² + b² = c²

Find hypotenuse: c = √(a² + b²)
Find leg a:      a = √(c² - b²)
Find leg b:      b = √(c² - a²)

Where a and b are the legs and c is the hypotenuse.

Worked examples:

The 3-4-5 rule in construction: to verify a right angle, measure 3 feet along one wall and 4 feet along the adjacent wall. The diagonal between those two points should be exactly 5 feet. This is the most widely used Pythagorean triple in practice.