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Unit Vector Calculator

Work out unit vector instantly with clear inputs, formula shown and shareable results.

About Unit Vector Calculator

Normalising divides a vector by its own magnitude, leaving the direction unchanged and the length equal to 1. Multiplying that unit vector by any value gives a vector of exactly that length in the same direction.

Formula

Unit vector

û = v / |v|, where |v| = √(x² + y² + z²)

Worked example

With the default values below, Unit Vector Calculator returns Unit vector of (0.230769, 0.307692, 0.923077). Change any input above and every figure here is recalculated in your browser.

Inputs used

Vector (x, y, z)
3, 4, 12
Rescale to this lengthminimum 0
1

Results

Unit vector
(0.230769, 0.307692, 0.923077)
Original magnitude
13.00000000
Rescaled to your length
(0.230769, 0.307692, 0.923077)
Length of the unit vector (should be 1)
1.00000000

Step by step

  1. 1Values used
  2. 2Unit vector
  3. 3Unit vector= (0.230769, 0.307692, 0.923077)
  4. 4Original magnitude= 13.00000000
  5. 5Rescaled to your length= (0.230769, 0.307692, 0.923077)
  6. 6Length of the unit vector (should be 1)= 1.00000000

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Normalise (3, 4, 12).

The magnitude is 13, so the unit vector is (3/13, 4/13, 12/13) ≈ (0.2307692, 0.3076923, 0.9230769).

Why can't the zero vector be normalised?

It has no direction and dividing by its zero length is undefined.

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