Your data
Paste a table straight from Excel or Google Sheets, or drop a CSV file. Nothing is uploaded anywhere — the whole calculation runs inside this browser tab.
CSV, TSV or plain text. Files saved in windows-1251 are detected and re-read automatically, so Cyrillic headers do not turn into garbage.
Parsing options
Columns
Result
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The drawing library is downloaded only when you press the button, and only on this page.
This page has no server side at all. The table you paste is parsed by JavaScript inside your own browser, the chart is drawn on a canvas element on your machine, and the export file is assembled locally. Nothing is uploaded, stored or written to any log. You can disconnect from the network after the page has loaded and everything will still work — which is the simplest way to verify the claim yourself.
Facts and limits of this method
| Formula | z = (value − mean) / standard deviation |
|---|---|
| Standard deviation used | Sample, divisor n−1 |
| Resulting mean | Exactly 0 by construction |
| Resulting standard deviation | Exactly 1 by construction |
| Counts reported | How many rows lie beyond ±2σ and beyond ±3σ |
| Minimum rows | 2, and the spread must be non-zero |
When it misleads you
- Standardising does not make data normal. It moves and rescales the distribution but leaves its shape untouched: a skewed column standardised is still skewed, and the familiar percentages attached to z-scores do not apply to it.
- Both ingredients are sensitive to outliers. One extreme value pulls the mean towards it and inflates the standard deviation, which shrinks the z-score of that very value and of everything else. For outlier hunting the IQR rule is the more reliable instrument.
- On small samples the range of possible z-scores is mathematically bounded. With n rows no value can exceed (n−1)/√n, which is about 4.2 at twenty rows — so "no z-score above 3" can mean the data is clean or simply that the sample is too small to produce one.
- A z-score is only comparable across datasets if both distributions have a similar shape. Comparing a z of 2 in a normal column with a z of 2 in a heavily skewed one is comparing two different things.
How it is calculated
The mean and the sample standard deviation are computed from the valid values in the column. Each value is then reduced by the mean and divided by the standard deviation, which recentres the data on zero and rescales it so that one unit equals one standard deviation.
By construction the resulting column always has a mean of exactly zero and a standard deviation of exactly one. That is not a coincidence to verify, it is the definition — which is why standardised values from different sources can be placed on the same axis.
The counts beyond ±2σ and ±3σ are reported because they are the quickest sanity check available. In a normal distribution about 5% of values fall beyond two standard deviations and about 0.3% beyond three; numbers far from those hint that the distribution is not normal.
If every value in the column is identical the standard deviation is zero, division is undefined, and the tool says so rather than returning zeros or infinities. That case is rare in measurements and common in columns that turn out to be constants.
Questions and answers
What counts as a high z-score?
Beyond ±2 is unusual and beyond ±3 is rare, but those thresholds come from the normal distribution. Check the normality tool first — on skewed data they mean much less than they appear to.
Why is the mean of my z-scores exactly zero?
Because subtracting the mean from every value forces it to be. It is a property of the transformation, not a finding about your data.
Can I use z-scores to compare two different columns?
Yes, and that is their main purpose — a z of 1.2 means the same relative position in both. The caveat is that the comparison only holds if the two distributions have a similar shape.
Should I use z-scores or the IQR rule to find outliers?
The IQR rule, because it is not distorted by the outliers themselves. Use z-scores to describe how extreme a value is once you have found it.
Is my data uploaded?
No. The standardisation runs in your browser and nothing is transmitted.