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Unit Vector Calculator

v̂ = v / |v| in 2 to 10 dimensions, with |v| as a simplified radical, each component exact (−3,6,−2 gives −3/7, 6/7, −2/7), the share each component takes of |v|², the direction cosines and a unit-circle figure.

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Unit Vector Calculator works straight from this page — free, instant, nothing to install. It covers −3,6,−2 gives −3/7, 6/7, −2/7 — adjust any of them and the result follows immediately.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Unit Vector Calculator do?

v̂ = v / |v| in 2 to 10 dimensions, with |v| as a simplified radical, each component exact (−3,6,−2 gives −3/7, 6/7, −2/7), the share each component takes of |v|², the direction cosines and a unit-circle figure.

What does it take into account?

It factors in −3,6,−2 gives −3/7, 6/7, −2/7. Change any of them and the output follows immediately.

When would I actually use this?

Checking a decomposition done by hand, solving a linear system, and finding the eigenvalues that describe how a transformation stretches space.

What is the most common mistake?

Inverting a matrix to solve a system. Elimination or a factorisation is both faster and far more stable numerically; an explicit inverse amplifies rounding error, especially when the matrix is close to singular.

How is Unit Vector Calculator different from Vector magnitude calculator?

They sit next to each other but answer different questions: Vector magnitude calculator is the one to open when you need it to compute the magnitude (length) of a 3D vector from its components. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Interactive Unit Circle Visualizer is the closest one after this: Drag around the circle and watch all six functions move with the angle, in degrees and radians. Special angles give their exact values — √3/2, not 0.866 — the quadrant signs are named, and tan at 90° says undefined instead of printing a huge number.

What else is worth having open alongside it?

Angle Between Two Vectors Calculator and Column Space Calculator (basis of Col(A), rank, pivot columns) — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The decompositions follow their textbook definitions with partial pivoting where it applies. Results are exact for small integer matrices and subject to floating-point rounding otherwise.

Further reading

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ExplainerThe Ideal Gas Law Explained: PV = nRT, R in Every Unit, and Where It BreaksPV = nRT holds when the gas is dilute and far from condensing. The value of R depends entirely on the units you feed it, and the temperature is never in degrees Celsius.How-toHow to Compare Unit Prices and Find the Better DealTurn any package price into a price per pound or ounce so you can compare sizes and brands honestly, ignore the marketing, and spot the real bargain on the shelf.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.ExplainerFibonacci and the Golden RatioThe Fibonacci sequence adds each pair of terms to make the next; the ratio of neighboring terms homes in on the golden ratio φ ≈ 1.618. See how, and where the pattern turns up.ExplainerWhat Is a Z-Score? Standard Deviations Above the MeanA z-score is z = (x − μ) / σ — how many standard deviations a value sits from the mean. Learn how to compute it, read the standard normal curve, and turn it into a percentile.