When to use this calculator
This extends the plane-distance formula with a third coordinate, useful for spatial measurements and 3D work.
Explore the coordinate & vector calculators for other questions in this topic. For a related calculation, use the Vector Cross Product Calculator: Find the three components of the cross product of two 3D vectors.
PUTTING IT INTO PRACTICE
Three Dimensional Distance: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| First x | 0 |
| First y | 0 |
| First z | 0 |
| Second x | 2 |
| Second y | 3 |
| Second z | 6 |
| Result | 7 units |
- Check the input labels and enter the example values above.
- Apply the relationship: Distance = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²).
- The result is 7 units, rounded for display.
How to interpret your result
Use the same linear unit for every coordinate.
Keep coordinate units consistent along every axis. Distance is non-negative, while slope and dot product can have signs. A vertical line has undefined slope because the horizontal coordinate change is zero.
Frequently asked questions
Does a zero dot product always mean the vectors are perpendicular?
Two nonzero vectors with zero dot product are perpendicular. The zero vector needs separate treatment because it has no defined direction.
When is the three dimensional distance calculator useful?
This extends the plane-distance formula with a third coordinate, useful for spatial measurements and 3D work.
How do I use the three dimensional distance calculator?
Enter first x, first y, first z, second x, second y, second z. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Distance = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²).
What should I check before using the result?
Use the same linear unit for every coordinate.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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