Pythagorean Theorem Calculator
Calculate the hypotenuse or any side of a right triangle using the Pythagorean theorem. Ideal for students and builders.
Pythagorean Theorem Calculator
Calculate missing side of a right triangle
Pythagorean Theorem:
a² + b² = c²
Where c is the hypotenuse (longest side)
Result
Calculated side length
Hypotenuse (c)
5
√(3² + 4²) = √(9 + 16) = 5
Triangle Properties
Triangle Type:Right Triangle
Area:6
Perimeter:12
Understanding the Pythagorean Theorem
The Pythagorean theorem is one of the most fundamental principles in geometry, stating that in a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides.
The Formula: a² + b² = c²
- a and b are the lengths of the two legs (shorter sides)
- c is the length of the hypotenuse (longest side, opposite the right angle)
How to Use This Calculator
- Choose whether you want to find the hypotenuse or a leg
- Enter the known side lengths
- Click calculate to get the missing side
- Use the verify mode to check if three sides form a right triangle
Real-World Applications
Construction & Architecture
- Ensuring walls are perpendicular
- Calculating roof slopes and rafter lengths
- Determining diagonal bracing requirements
- Foundation layout and squaring
Navigation & Engineering
- GPS distance calculations
- Surveying and mapping
- Electrical circuit design
- Computer graphics and game development
Common Pythagorean Triples
Basic Triples
- 3, 4, 5
- 5, 12, 13
- 8, 15, 17
- 7, 24, 25
Scaled Triples
- 6, 8, 10 (2×3,4,5)
- 9, 12, 15 (3×3,4,5)
- 10, 24, 26 (2×5,12,13)
- 15, 20, 25 (5×3,4,5)
Large Triples
- 20, 21, 29
- 12, 35, 37
- 28, 45, 53
- 16, 63, 65