Pythagorean Theorem Calculator
Calculate the sides of a right triangle with our easy-to-use Pythagorean Theorem calculator.
Understanding the Pythagorean Theorem
Our Pythagorean Theorem Calculator allows you to quickly determine the sides of a right triangle using the famous formula a² + b² = c². This tool is perfect for students, engineers, architects, and anyone working with right triangles.
What is the Pythagorean Theorem?
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of squares of the other two sides (a and b).
a² + b² = c²
Named after the ancient Greek mathematician Pythagoras, this theorem is one of the fundamental principles in geometry and has countless applications in various fields.
Applications of the Pythagorean Theorem:
In Mathematics:
- Geometry problems
- Distance calculations
- Coordinate geometry
- Trigonometry
- Vector mathematics
In Real-World Applications:
- Construction and architecture
- Navigation and GPS systems
- Land surveying
- Engineering design
- Physics calculations
How to Use the Calculator:
- Select what you want to calculate (hypotenuse or one of the legs)
- Enter the values for the known sides
- Choose the appropriate unit of measurement
- Select your preferred decimal precision
- Click "Calculate" to see all results
Interesting Facts About the Pythagorean Theorem
- Ancient Knowledge: Evidence suggests that civilizations like the Babylonians and Egyptians knew about this relationship before Pythagoras, but he is credited with the first proof
- Pythagorean Triples: These are sets of three integers that satisfy the Pythagorean Theorem, such as 3-4-5, 5-12-13, and 8-15-17
- Extended Applications: The theorem extends to higher dimensions and non-Euclidean geometries
- Many Proofs: There are over 400 different proofs of the Pythagorean Theorem, including one by President James Garfield
- Converse Theorem: If a² + b² = c², then the triangle with sides a, b, and c is a right triangle (with the right angle opposite side c)