Vector Magnitude Calculator

Solve |v| = √(x² + y² + z²) ; v̂ = v/|v| step by step — free vector magnitude calculator with worked examples, real-world defaults and instant answers.

|v| = √(x² + y² + z²) ; v̂ = v/|v|

xyz

Magnitude |v|10

Unit vector v̂(0.6, 0.8, 0)

1
Pythagoras in as many dimensions as you have:
|v| = √(6² + 8² + 0²) = √100 = 10
2
Divide each component by the magnitude to get the pure direction:
v̂ = (6, 8, 0) / 10 = (0.6, 0.8, 0)
3
Check — a unit vector has length exactly 1:
|v̂| = 1 ✓

Every vector factors into magnitude × direction — normalizing strips the size so only direction remains. Unit vectors are everywhere: surface normals in graphics, direction cosines in mechanics, normalized features in ML. Default (6, 8, 0) has the friendly length 10.

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Vector magnitude & unit vector — length and direction split apart.

About Vector Magnitude Calculator

The Vector Magnitude Calculator solves |v| = √(x² + y² + z²) ; v̂ = v/|v| for you with the full working shown — every substitution, every unit, every step, exactly the way a good teacher writes it on the board. Every vector factors into magnitude × direction — normalizing strips the size so only direction remains.

How to use Vector Magnitude Calculator

1Enter your known values in the input fields (sensible real-world defaults are pre-filled).
2The tool substitutes them into |v| = √(x² + y² + z²) ; v̂ = v/|v| and recomputes live.
3Read the answer in the result box, then expand the step-by-step solution to see the full working.
4Copy the method into your notebook, or change inputs to explore how the result behaves.

Why use Vector Magnitude Calculator?

✓Solves |v| = √(x² + y² + z²) ; v̂ = v/|v| instantly as you type — no submit button, no waiting
✓Step-by-step solution shown for every calculation, not just the final answer
✓Realistic example values pre-loaded so you can see a worked example immediately
✓100% free, no sign-up, runs entirely in your browser — your numbers never leave your device
✓Mobile-friendly and fast enough to use mid-homework or mid-lesson

Frequently asked questions

What formula does the Vector Magnitude Calculator use?+

It uses |v| = √(x² + y² + z²) ; v̂ = v/|v|. The steps section shows the formula with your actual numbers substituted, so you can follow (and verify) every stage of the calculation rather than trusting a black box.

What should I keep in mind when using this calculator?+

Is the Vector Magnitude Calculator free to use?+

Completely free, with no sign-up or limits. All computation happens client-side in your browser, so it is fast, private, and works even on slow connections once the page has loaded.

Can I use this for homework, teaching or exam prep?+

That is exactly what it is built for. The step-by-step working mirrors how solutions are presented in class, so you can check homework, build worked examples for teaching, or practise method recall before exams.

Embed Vector Magnitude Calculator on your website

Want Vector Magnitude Calculatoron your own site? Paste this snippet into any HTML page — it's free, with no API key or sign-up. The tool loads in an iframe and keeps working exactly as it does here.

Embed code

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