Formula Explanation
|v| = sqrt(x^2 + y^2 + z^2)
This calculator applies the formula |v| = sqrt(x^2 + y^2 + z^2). Enter each value with the matching unit, and AZCalculate updates the result instantly.
Scientific
Vector Calculator
Use this vector calculator to calculate calculate vector magnitude, dot product, and component sums for 3d vectors.
vectormagnitudedot product3d
Calculator
Calculate instantly
Calculator Inputs
Choose what you want to calculate, enter realistic values, adjust units where shown, and use the scenario section for repeated-use planning.
Input and Formula Breakdown
This calculator applies the formula |v| = sqrt(x^2 + y^2 + z^2). Enter each value with the matching unit, and AZCalculate updates the result instantly.
Vector A x
3
Vector A y
4
Vector A z
5
Vector B x
2
Vector B y
1
Vector B z
6
Magnitude A
7.07
Magnitude B
6.4
Dot product
40
Scenario and Comparison
Current
7.07
Projected
84.85
Adjusted
7.78
Visual Comparison
Current result7.07
Projected usage84.85
Comparison scenario7.78
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Use Cases
- Analyze vectors
- Check physics components
- Study linear algebra
Step-by-Step Explanation
- Step 1Enter the known values in the calculator fields.
- Step 2Keep the units consistent with the labels shown beside each input.
- Step 3Apply the formula: |v| = sqrt(x^2 + y^2 + z^2).
- Step 4Review the primary result and supporting values.
Example calculation
Example vector calculator
Given
- Vector A x: 3
- Vector A y: 4
- Vector A z: 5
- Vector B x: 2
- Vector B y: 1
- Vector B z: 6
Steps
- Use the values shown above.
- Apply |v| = sqrt(x^2 + y^2 + z^2).
Result
The calculator above shows the computed answer instantly from these example values.
Calculator guide
About this Vector Calculator
Calculate vector magnitude, dot product, and component sums for 3D vectors. This page includes an interactive calculator, concise formula notes, worked examples, FAQs, related calculators, and practical guidance you can revisit whenever needed.
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Calculator usage
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Total visits today
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Live users now
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Total saved calculations
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Most active date
2026-06-05
FAQ
Vector Calculator FAQs
How does the vector calculator work?+
It uses |v| = sqrt(x^2 + y^2 + z^2) and calculates the result from the values you enter.
Can I copy or print the result?+
Yes. AZCalculate calculator pages include copy, share, and print actions.
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