What Is the Pythagorean Theorem?
The Pythagorean Theorem relates the three sides of a right triangle: the square of the hypotenuse (the longest side, opposite the right angle) equals the sum of the squares of the other two sides (the legs).
How to Use the Pythagorean Theorem Calculator
- Choose whether to find the hypotenuse or a missing leg.
- Enter the two known side lengths.
- The missing side calculates instantly.
Pythagorean Theorem Formula
Worked Example
c² = 3² + 4² = 9 + 16 = 25
c = √25 = 5
This is the classic "3-4-5" right triangle.
Understanding Your Results
The Pythagorean Theorem only applies to right triangles (triangles with exactly one 90° angle). The hypotenuse is always the longest side and is always opposite the right angle.
Real-World Uses
- Construction: checking that corners are square, calculating diagonal bracing lengths.
- Navigation: finding straight-line distance between two points.
- Screen sizes: TV and monitor diagonal measurements use this theorem (width and height as the legs).
Common Mistakes to Avoid
- Applying the theorem to non-right triangles, where it doesn't hold.
- Mixing up which side is the hypotenuse — it must be the longest side, opposite the right angle.
- Forgetting to take the square root after summing the squares.
Frequently Asked Questions
It calculates the length of a missing side of a right triangle, given the other two sides — used widely in construction, navigation, and geometry.
No — it only applies to right triangles, which have exactly one 90-degree angle.
Rearrange the formula to a = √(c² − b²), using the hypotenuse and the other known leg.
A set of three whole numbers that satisfy a² + b² = c², like 3-4-5 or 5-12-13 — useful reference triangles in geometry.
A TV or monitor's advertised size is its diagonal measurement, calculated using the theorem with the screen's width and height as the two legs.