3D Distance Calculator

Calculate the spatial distance between two points in three-dimensional space

Note: This calculator uses the 3D Euclidean distance formula. For other distance metrics (like Manhattan or Chebyshev), different formulas apply.

Tip: Enter coordinates as numbers (positive or negative). The calculator works in any consistent unit system.

Point A (x₁, y₁, z₁)

X-coordinate

Y-coordinate

Z-coordinate

Point B (x₂, y₂, z₂)

X-coordinate

Y-coordinate

Z-coordinate

Distance Metric

Euclidean Distance (Standard 3D distance)

Manhattan Distance (Taxicab in 3D)

Chebyshev Distance (Maximum axis difference)

Understanding 3D Distance Metrics

Euclidean Distance

The straight-line distance through 3D space
Extension of Pythagorean theorem to 3D
Formula: √((x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²)
Most common for physical distances

Manhattan Distance

Sum of absolute differences along axes
Formula: |x₂-x₁| + |y₂-y₁| + |z₂-z₁|
Represents grid-based movement distance
Useful for certain pathfinding algorithms

Chebyshev Distance

Maximum difference along any single axis
Formula: max(|x₂-x₁|, |y₂-y₁|, |z₂-z₁|)
Represents movement where any direction can be combined
Used in chess for king movement distance

3D Distance Applications

3D Modeling & Animation: Calculating distances between objects in 3D space for collision detection and movement.

Engineering & Architecture: Determining spatial relationships in structural designs and mechanical parts.

Physics & Astronomy: Measuring distances between particles in 3D simulations or celestial bodies in space.

Frequently Asked Questions

What's the difference between 2D and 3D distance calculations?

3D distance includes the z-axis component, making it suitable for spatial calculations. The Euclidean formula extends the 2D version by adding the squared z-difference: √(Δx² + Δy² + Δz²) instead of just √(Δx² + Δy²).

When should I use Manhattan distance in 3D?

Manhattan distance is useful in 3D grid-based systems (like voxel environments) where movement is restricted to axis-aligned directions, similar to navigating city blocks but in three dimensions.

Can I use this for GPS coordinates?

For very short distances (like within a city), this can approximate distances between GPS coordinates if you treat latitude as y, longitude as x, and altitude as z. However, for precise calculations over longer distances, you should use specialized geodetic formulas that account for Earth's curvature.

How do negative coordinates affect the calculation?

Negative coordinates work perfectly fine since all distance formulas use either squares (Euclidean) or absolute values (Manhattan, Chebyshev) of the differences. The distance is always a non-negative value.

What's the practical use of Chebyshev distance in 3D?

Chebyshev distance is valuable in 3D pathfinding where movement can occur simultaneously along multiple axes at the same speed (like a queen in 3D chess). It represents the minimal number of moves needed when movement in all directions is allowed.