ScanSpotStandard Deviation Calculator
Both standard deviations, labelled with the divisor, so you do not have to guess which one your answer wants.
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📊 Standard Deviation Calculator
Paste a list of numbers: sample and population standard deviation, both shown and labelled, with the sum of squares you would check by hand. Nothing leaves the browser.
Separate values with spaces, commas or new lines — a column pasted straight out of a spreadsheet works. Decimal points only: 1234.5, not 1,234.5.
Which one? Use the sample figure when your numbers are a sample of something larger, the population figure when they are the whole set. The two only disagree noticeably when there are few values.
Standard deviation is the average distance of your numbers from their mean, and almost every wrong answer comes from one of two places: dividing by n when the tool should divide by n − 1, or subtracting two very large numbers that nearly cancel. This calculator shows both figures with their divisors attached, and computes them in a way that survives a small spread around a large mean.
How to use the Standard Deviation Calculator
- Paste or type your numbers. Spaces, commas, semicolons and line breaks all separate values, so a column copied out of a spreadsheet can go straight in.
- Everything updates as you type: count, sum, mean, median, minimum and maximum, then the two standard deviations and the two variances.
- Read the sum of squares at the bottom if you want to check the result by hand — square each distance from the mean, add them up, divide, take the root.
Why people use it
- Both figures, not one. Tools that make you choose sample or population before showing a number are asking you to know the answer first; choosing wrong is the most common error in this calculation, and it is invisible afterwards — the wrong number looks exactly like the right one. The divisor is written into each label so the choice is checkable rather than memorised.
- The computation is two-pass. The textbook shortcut E[x²] − E[x]² subtracts two numbers around 10¹⁸ when your values are around 10⁹, and the small standard deviation you were looking for disappears into the rounding. Averaging first and then squaring the distances costs one extra loop and keeps that case right.
- It refuses instead of answering. A single value has no sample standard deviation — the divisor n − 1 is zero — and a spreadsheet answers #DIV/0!, which is at least honest, while a hand-rolled calculator often prints 0. This one prints a dash and one sentence saying why. The same applies to a mistyped value: it names the token instead of quietly dropping it.
Frequently asked questions
Which standard deviation should I use?
If your numbers are a sample drawn from something larger — a week of sales out of a year, one batch out of a production run — use the sample figure (divide by n − 1). If they are the entire set you care about — every student in the class, all twelve months — use the population figure (divide by n). When n is above roughly 30 the difference is small, but for a handful of values it is large enough to be marked wrong.
Why is the sample figure always the larger one?
Because it divides the same sum of squares by a smaller number. Both start from the sum of squared distances to the mean; the sample version divides by n − 1 and the population version by n. With ten values that is a 11% larger variance and about 5% larger standard deviation — and the gap shrinks as n grows, which is why the two are quoted to the same number of decimal places here.
What happens if I enter only one number?
The population standard deviation is 0 by definition — one value is exactly its own mean, so nothing deviates. The sample standard deviation does not exist: its divisor is n − 1 = 0. This calculator shows a dash for the sample figures and says so in a sentence, rather than dividing by zero and printing 0.
Can it handle a column pasted from Excel or Google Sheets?
Yes. Line breaks, spaces, commas and semicolons all separate values, and the ideographic comma and full-width space that CN/JP keyboards produce are treated the same way. Thousands separators are not: 1,234.5 is read as two numbers, 1 and 234.5, so paste the plain number instead. Up to 100,000 values at a time.