Free calculator
Standard deviation calculator
Paste a list of numbers (from Google Sheets, Excel, or plain text) and choose sample or population. You get count, mean, variance, and standard deviation, with optional step-by-step deviations for small lists. The Google Sheets & Excel block below uses STDEV.S / STDEV.P and matching variance functions for each mode.
When to use this calculator
Quick descriptive stats before you move the same logic into a workbook—transparent formulas, not a statistics suite.
- Classroom or self-study checks for mean, variance, and SD with explicit sample vs population.
- Sanity-check a column you pasted from Sheets or Excel against
STDEV.S/STDEV.P. - See whether spread is zero (all identical values) or meaningful before modeling volatility elsewhere.
- Copy the spreadsheet patterns below when you need the same denominator convention (n vs n − 1) in cells.
Start from your numeric list. The mean is the average; each deviation is value − mean; variance is the average of squared deviations with denominator n (population) or n − 1 (sample); standard deviation is the square root of variance.
Mean
x = (sum of values) ÷ n. Every deviation compares a value to this center.
Sum of squared deviations
For each x, compute (x − x)2 and add them. This sum (SS) feeds both variance formulas below.
Variance and denominator
Population variance uses SS ÷ n. Sample variance uses SS ÷ (n − 1) (undefined when n < 2, which is why sample mode requires at least two values). Pick the mode that matches your workbook function (STDEV.P vs STDEV.S).
Standard deviation
SD = √variance. It has the same units as your original measurements (unlike variance, which is in squared units).
We do not model weighted observations, frequency tables, confidence intervals, or standard error of the mean—add those in a full statistics workflow when you need them.
For median, mode, and range on the same pasted list (without variance on this page), open the mean median mode range calculator.
Additional answers on this page cover spreadsheet match-ups, n − 1 intuition, and the difference from standard error of the mean (a different question from the list standard deviation shown here).
Google Sheets & Excel
In Google Sheets and in Microsoft Excel with English (US/UK) function names, use STDEV.S / STDEV.P for standard deviation and VAR.S / VAR.P for variance. Replace A1:A99 with your range. If your Excel is not in English, use Formulas → Insert function in Excel to find the same functions under your language pack’s own names.
=STDEV.S(A1:A99)Matches n − 1 in the denominator. In legacy spreadsheets you may still see STDEV—prefer STDEV.S for clarity.
=STDEV.P(A1:A99)Use when every member of the population is in the range (divide-by-n variance under the hood).
=VAR.S(A1:A99)Variance is standard deviation squared; VAR.S lines up with STDEV.S.
=VAR.P(A1:A99)Pairs with STDEV.P for the same n denominator convention.
Frequently asked questions
What is standard deviation?
A measure of spread around the mean. Small SD means values sit close to the average; large SD means they are more dispersed. It is the square root of variance (which is in squared units).
When should I use sample vs population?
Use population when your list is every member you care about (the whole class, every SKU in a fixed catalog). Use sample when the list is a subset you treat as drawn from a bigger population—common in science and A/B testing. The math differs only in the variance denominator (n vs n − 1).
What is the difference between variance and standard deviation?
Variance averages squared deviations; standard deviation is √variance. SD is easier to read because it shares the same units as your measurements.
Why divide by n − 1 for a sample?
With sample data, using n in the denominator usually underestimates spread. The n − 1 (Bessel) correction adjusts the average squared deviation so the variance tracks what you would expect from many repeated samples—standard in textbooks and in STDEV.S. Population mode matches STDEV.P (divide by n).
Which Google Sheets or English Excel function matches this page?
Sample mode aligns with STDEV.S and VAR.S. Population mode aligns with STDEV.P and VAR.P. Always pass the same numeric range you typed here.
What are the German Excel function names?
Typical Excel (Deutsch) pairs are STABW.S (Stichprobe, like STDEV.S) and STABW.N (Grundgesamtheit, like STDEV.P), with VAR.S / VAR.P for variance—confirm in your function library if your build differs.
What are the French Excel function names?
Typical Excel (français) names are ECARTYPE.ST (échantillon, like STDEV.S) and ECARTYPE.PE (population entière, like STDEV.P), with VAR.S / VAR.P variance counterparts—verify on your install.
How should I paste data from a spreadsheet?
Copy a column or row, paste into the box, and keep one number per cell as plain text. Tabs, newlines, spaces, semicolons, and many comma-separated lists work. Decimals can use . or , depending on how you type them—see skipped-token hints if something does not parse.
When is standard deviation zero?
When every value is identical, all deviations are 0, so variance and SD are 0. With population mode and n = 1, SD is also 0 by convention here.
Is this the standard error of the mean?
No. Standard error usually means SD of the sample mean, often SD / √n for simple random samples. This page reports SD of your list, not the sampling distribution of the mean.
Is this professional statistics advice?
No. It is a free educational calculator. For research protocols, quality systems, or regulated reporting, follow your organization’s methods and qualified experts.