Normalize a Vector
Create a unit vector (length = 1). Runs entirely in your browser, so your data never leaves your device.
0 chars · 0 lines
Output
The result appears here as you type.
How to use Normalize a Vector
- 1. Paste your vector. Enter one or more vectors, one per line, for example (3, 4). Each vector is divided by its own magnitude to produce a unit vector pointing in the same direction.
- 2. Set the decimal places. Choose Decimal places to control how many digits appear after the decimal point, since normalized components are usually irrational and need rounding for a readable result.
- 3. Copy the unit vector. The normalized vector, with a length of exactly 1, appears in the output pane. Copy it into your physics or graphics calculation wherever a direction-only vector is needed.
When to use Normalize a Vector
Normalize a Vector divides a vector by its own magnitude to produce a unit vector, one with length exactly 1 that preserves only the direction. Use it whenever a calculation needs direction independent of magnitude.
- Computing a lighting direction in graphics. A 3D rendering exercise needs the direction from a surface point to a light source as a unit vector before plugging it into a dot-product lighting equation, since the formula assumes unit length.
- Checking a physics homework normalization. A course problem asks you to find the unit vector in the direction of a given force or velocity vector, and you want to confirm your by-hand division by the magnitude is correct.
- Preparing direction vectors for a simulation. A physics or game simulation stores object headings as unit vectors, and converting raw displacement vectors into normalized form here avoids introducing a bug in a custom normalize function.
- Comparing angles between vectors. Before computing the angle between two vectors using the dot product formula, normalizing both first simplifies the arithmetic since the magnitudes drop out of the equation entirely.
Examples
Normalize a 2D vector
Input
(3, 4)
Output
(0.600000, 0.800000)
One vector per line
Input
(1, 2, 2) (0, 5, 0)
Output
(0.333333, 0.666667, 0.666667) (0.000000, 1.000000, 0.000000)
About the Normalize a Vector tool
Normalize a Vector runs as plain JavaScript in your browser tab, with no server behind it. Create a unit vector (length = 1). Whatever you put in stays on your device from start to finish.
The tool is part of EditSafely's Math Tools section, 234 single-purpose utilities built around the same idea: open the page, get the result, keep your data to yourself.
You can shape the output with the Decimal places setting, and the result refreshes the moment you change it. 2 worked examples further down the page show exactly what the tool produces for real inputs.
That local-first design has practical benefits beyond privacy. The tool keeps working on a flaky connection once the page has loaded, results are instant because nothing round-trips to a server, and it is safe to use with confidential material.
Frequently asked questions
Does Normalize a Vector cost anything?
Yes, it is completely free. All 2,658 tools on EditSafely work without an account, a subscription or usage limits.
Is it safe to paste sensitive or confidential data?
No data leaves your device. The whole tool is JavaScript that runs inside your browser tab, so there is no upload, no server-side processing and no log of what you did. If you disconnect from the internet after the page loads, it keeps working.
How much text can I process at once?
There is no fixed limit. Because the work happens on your own device rather than on a shared server, the practical ceiling is your machine's memory, which comfortably handles inputs far larger than typical online tools allow.
Do I need to sign up or install anything?
Nothing to install and no account needed. Open the page in any up-to-date browser, including on a phone or tablet, and the tool is ready.
How do I use the result?
The output panel has a one-click copy button, and you can keep refining the input while you work; the result updates in place as you type.