When to use this calculator
Find the length of a three-dimensional vector. Components must use the same unit and perpendicular coordinate axes.
Explore the coordinate & vector calculators for other questions in this topic. For a related calculation, use the Kite Area Calculator: Find the area of a simple kite from its perpendicular diagonals.
PUTTING IT INTO PRACTICE
Vector Magnitude: 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 |
|---|---|
| X component | 2 |
| Y component | 3 |
| Z component | 6 |
| Result | 7 component units |
- Check the input labels and enter the example values above.
- Apply the relationship: Magnitude = √(x²+y²+z²).
- The result is 7 component units, rounded for display.
How to interpret your result
Components must use the same unit and perpendicular coordinate axes.
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 vector magnitude calculator useful?
Find the length of a three-dimensional vector. Components must use the same unit and perpendicular coordinate axes.
How do I use the vector magnitude calculator?
Enter x component, y component, z component. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Magnitude = √(x²+y²+z²).
What should I check before using the result?
Components must use the same unit and perpendicular coordinate axes.
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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