Pythagorean Theorem Calculator
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How to Use This Tool
This calculator helps you solve missing side lengths for right-angled triangles instantly. Manual calculations with square roots can be slow—this tool automates the process using the Pythagorean Theorem formula.
The Formula
The theorem states that for any right triangle (with a 90° angle), the square of the hypotenuse is equal to the sum of the squares of the two legs.
a² + b² = c²
How the Math Works
Depending on which side you are trying to find, the formula rearranges:
| Solve For | Formula | Example (3-4-5 Triangle) |
|---|---|---|
| Hypotenuse (c) | c = √(a² + b²) | √(3² + 4²) = 5 |
| Leg (a) | a = √(c² - b²) | √(5² - 4²) = 3 |
| Leg (b) | b = √(c² - a²) | √(5² - 3²) = 4 |
Real-World Uses
- Carpentry: Use the "3-4-5 Rule" to verify corners are perfectly square.
- Ladders: Determine the safe ladder length needed to reach a specific roof height.
- Displays: Calculate the actual width/height of a TV based on its diagonal screen size.