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
Save and share
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
| Sample formula | Divisor n−1. This is Excel STDEV.S and the default in almost every statistics course. |
|---|---|
| Population formula | Divisor n. Use it only when your rows are the entire population, not a sample of it. |
| Both shown | Always, side by side — the difference between them is the most common source of mismatched results. |
| Also returned | Variance for both divisors, the mean, the count and the standard error of the mean. |
| Minimum rows | 2 for the sample formula, 1 for the population formula. |
| Units | Same as your data, unlike variance which is in units squared. |
When it misleads you
- Standard deviation assumes the spread is roughly symmetric around the mean. On skewed data it describes a shape that is not there, and the interquartile range from the quartiles tool is the honest alternative.
- One extreme value inflates it dramatically, because deviations are squared before averaging. A single wrong row can double the standard deviation while leaving the median untouched.
- The familiar "68% within one standard deviation" holds only for a normal distribution. Check the normality tool before quoting it — on skewed or heavy-tailed data the real percentage can be far from 68.
- It cannot be compared across different units or wildly different scales. For that you need the coefficient of variation, which divides it by the mean and drops the units.
How it is calculated
Each value is compared to the mean, the difference is squared, and the squares are averaged. Squaring is what makes deviations in both directions count as spread rather than cancelling out, and it is also why one large deviation dominates: at four times the distance it contributes sixteen times the weight.
The sample formula divides by n−1 rather than n. The reason is that the mean was itself estimated from the same data, so the deviations are slightly too small on average; dividing by a smaller number corrects the bias. This is what Excel STDEV.S returns and what "standard deviation" means in a statistics course unless the word "population" appears.
The population formula divides by n. Use it only when your rows really are everything — every employee in the company, every machine on the floor — and not a sample from a larger group. In practice that is rarer than people assume.
The standard error of the mean is the standard deviation divided by the square root of the count. It answers a different question: not how spread out the values are, but how precisely the mean itself is pinned down. It shrinks as you collect more data, while the standard deviation does not.
Questions and answers
Which number should I use, n−1 or n?
Use n−1 unless your rows are the entire population. Sampled data — a month of orders, a survey, a batch of measurements — always takes n−1. Both are shown so you never have to guess which one a tool used.
Why does my result differ from another calculator?
Almost always the divisor. Many school-oriented calculators default to n. Compare against both numbers on this page and the discrepancy will resolve immediately.
Is a standard deviation of 5 large?
Only in relation to the mean. Five minutes on a twenty-minute delivery is large; five minutes on a twenty-hour shipment is nothing. The coefficient of variation makes that comparison directly.
What is the standard error and why is it so much smaller?
It measures the precision of the mean rather than the spread of the values, and it falls as the square root of the count. With 25 rows it is five times smaller than the standard deviation.
Does my data leave the browser?
No. There is no server; the calculation happens on your device.