Pythagorean Theorem Calculator

Calculate missing sides of right triangles using the Pythagorean theorem. Essential for mathematics, engineering, and construction.

How to Use Pythagorean Theorem Calculator

1. 1.**Enter any two values**: two sides or one side and hypotenuse
2. 2.**Click "Calculate"** to find the missing value
3. 3.**View results** for all triangle sides
4. 4.**Check if triangle is valid** with your inputs

Features

• •**Multiple Inputs**: Use any two known values
• •**Automatic Calculation**: Find missing side or hypotenuse
• •**Validation**: Check if triangle is possible
• •**Real-time Results**: Instant calculations

Pythagorean Theorem Formula

a² + b² = c²

Where:

• •**a** and **b** are the two shorter sides (legs)
• •**c** is the longest side (hypotenuse)

Common Applications

• •**Construction**: Squaring buildings, roof pitch, stairs
• •**Engineering**: Force vectors, structural analysis
• •**Navigation**: Distance calculations, triangulation
• •**Computer Graphics**: 2D positioning, collision detection
• •**Surveying**: Land measurement, property boundaries

Pythagorean Triples

Common integer solutions:

• •**3-4-5**: 3² + 4² = 5² (9 + 16 = 25)
• •**5-12-13**: 5² + 12² = 13² (25 + 144 = 169)
• •**8-15-17**: 8² + 15² = 17² (64 + 225 = 289)
• •**7-24-25**: 7² + 24² = 25² (49 + 576 = 625)

Practical Examples

• •**TV Screen**: 32" diagonal, 24" width = 21.2" height
• •**Ladder**: 10ft ladder, 6ft from wall = 8ft reach
• •**Roof**: 8ft rise, 12ft run = 14.4ft rafter length
• •**Diagonal**: 6ft × 8ft room = 10ft diagonal

Tips for Using Pythagorean Calculator

• •**Enter any two values** to find the third
• •**Use consistent units** for all measurements
• •**Check for valid triangles** (hypotenuse must be longest)
• •**Round appropriately** for practical applications
• •**Consider real-world constraints** (material thickness, etc.)

Triangle Validation

For a valid right triangle:

• •**c² = a² + b²** must be true
• •**c** must be the longest side
• •**All sides** must be positive numbers
• •**Triangle inequality**: a + b > c must be true

Advanced Applications

• •**3D Distance**: Extend to 3D coordinates
• •**Vector Mathematics**: Calculate resultant vectors
• •**Physics**: Force and velocity components
• •**Signal Processing**: Phase relationships