📐 Three-Dimensional Distance Calculator
Calculate distance between two points in 3D space
Point 1 (x₁, y₁, z₁)
Point 2 (x₂, y₂, z₂)
How to Use This Calculator
Enter Point 1 Coordinates
Input the x, y, and z coordinates (x₁, y₁, z₁) of the first point.
Enter Point 2 Coordinates
Input the x, y, and z coordinates (x₂, y₂, z₂) of the second point.
Calculate
Press "Calculate Distance" to find the Euclidean distance between the two points in 3D space.
Formula
3D Distance = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)
Extension of 2D distance formula to include z-coordinate
Example: Points (1, 2, 3) and (4, 5, 6)
d = √((4-1)² + (5-2)² + (6-3)²)
= √(3² + 3² + 3²) = √27 = 3√3 ≈ 5.196
About Three-Dimensional Distance Calculator
The Three-Dimensional Distance Calculator finds the Euclidean distance between two points in 3D space. It extends the 2D distance formula by adding the z-coordinate component.
When to Use This Calculator
- 3D Geometry: Calculate distances in 3D space
- Physics: Find distances between 3D points
- Engineering: Measure distances in 3D designs
- Computer Graphics: Calculate 3D distances for rendering
- Architecture: Measure distances in 3D building plans
Understanding 3D Distance
3D distance extends the Pythagorean theorem to three dimensions. It measures the straight-line distance between two points in 3D space, accounting for all three coordinate differences.
Frequently Asked Questions
How is 3D distance calculated?
3D distance uses the formula: d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²). It's the 3D extension of the Pythagorean theorem, adding the z-coordinate difference.
What's the difference from 2D distance?
2D distance uses only x and y coordinates: d = √((x₂ - x₁)² + (y₂ - y₁)²). 3D distance adds the z-coordinate: d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²).
Is 3D distance always positive?
Yes! Distance is always non-negative. It represents the magnitude of the separation between two points, regardless of direction. Zero distance means the points coincide.