Overview
The Pythagorean theorem relates the sides of a right triangle: the square of the hypotenuse equals the sum of the squares of the other two sides. It is used in measurement, construction, navigation and drawing, and underlies the distance formula in the plane.
Formula
a² + b² = c², where c is the hypotenuse and a and b are the legs.
How it works
Identify the legs
The two perpendicular sides are a and b.
Square each leg
Compute a² and b².
Add and take the root
c = √(a² + b²).
Verify
Confirm the hypotenuse is longer than each leg.
Worked examples
Example 1: 3 and 4
c = √(9 + 16) = √25 = 5.
Example 2: 6 and 8
c = √(36 + 64) = √100 = 10.
Frequently asked questions
Can I find a leg from the hypotenuse?
Yes, using a = √(c² − b²) when the hypotenuse and the other leg are known.
What is a Pythagorean triple?
Three whole numbers satisfying the theorem, such as 3, 4, 5 or 5, 12, 13.
Does it apply to any triangle?
No, only to right triangles. For other triangles use the law of sines or the law of cosines.
This calculator is for educational and informational purposes only and is not a substitute for professional advice.