Pythagorean Theorem Calculator
Calculate missing sides of right triangles using a² + b² = c². Find the hypotenuse or legs with instant solutions.
Pythagorean Theorem Calculator
a² + b² = c²
Where c is the hypotenuse and a, b are the legs
About the Pythagorean Theorem
The Pythagorean theorem is one of the most famous mathematical formulas. It describes the relationship between the sides of a right triangle and has countless practical applications.
The Formula
- a² + b² = c²
- a and b are the legs (shorter sides)
- c is the hypotenuse (longest side, opposite the right angle)
- Works only for right triangles (90° angle)
Common Applications
- Construction: Ensuring corners are square
- Navigation: Calculating direct distances
- Engineering: Structural design and analysis
- Computer graphics: Distance calculations
- Physics: Vector calculations and force analysis
Historical Context
- Named after ancient Greek mathematician Pythagoras
- Known to Babylonians 1000 years before Pythagoras
- Has over 400 different proofs
- Foundation for trigonometry and coordinate geometry
Pythagorean Triples
- (3, 4, 5) - Most common triple
- (5, 12, 13) - Often used in construction
- (8, 15, 17) - Another popular triple
- (7, 24, 25) - Useful for larger measurements