Pythagorean Theorem Calculator
Calculate missing sides of right triangles using the Pythagorean theorem (a² + b² = c²) with step-by-step calculations. Perfect for geometry, construction, and engineering applications.
Right Triangle Calculator
Common Pythagorean Examples
Click on these links to see instant calculations with common right triangles:
Pythagorean Theorem
The Pythagorean theorem is a fundamental principle in geometry that relates the three sides of a right triangle. It states that the square of the hypotenuse equals the sum of squares of the other two sides.
Pythagorean Theorem Formula
Where:
a, b = legs (shorter sides)
c = hypotenuse (longest side)
To find c: c = √(a² + b²)
To find a: a = √(c² - b²)
Common Pythagorean Triples
| Side a | Side b | Hypotenuse c | Triangle Type |
|---|---|---|---|
| 3 | 4 | 5 | 3-4-5 Triangle |
| 5 | 12 | 13 | 5-12-13 Triangle |
| 8 | 15 | 17 | 8-15-17 Triangle |
| 7 | 24 | 25 | 7-24-25 Triangle |
| 1 | 1 | √2 ≈ 1.414 | 45-45-90 Triangle |
- Construction: Calculate diagonal distances, roof slopes, and structural measurements
- Navigation: Find direct distances and shortest paths between points
- Engineering: Design right-angled structures and calculate force vectors
- Mathematics: Solve geometry problems and triangle calculations
- Real Estate: Calculate property dimensions and lot measurements
Frequently Asked Questions
What is the Pythagorean theorem?
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (longest side) equals the sum of squares of the other two sides: a² + b² = c², where c is the hypotenuse.
How do you find the hypotenuse of a right triangle?
To find the hypotenuse, use the formula c = √(a² + b²), where a and b are the lengths of the two shorter sides. For example, if a = 3 and b = 4, then c = √(9 + 16) = √25 = 5.
When do you use the Pythagorean theorem?
Use the Pythagorean theorem for right triangles (triangles with a 90° angle) to find missing side lengths when you know two sides. It's used in construction, navigation, engineering, and many real-world applications.