Both formulas, one click apart
The n − 1 sample formula and the n population formula give different answers on small datasets. Switch and see.
Tools / Standard Deviation Calculator
Standard Deviation Calculator
Paste a list of numbers, choose sample or population, and get the standard deviation with variance, mean, and range alongside it.
s = √( Σ(x − x̄)² ÷ (n − 1) ) for a sample · σ divides by n
Paste numbers to see the result
- 1
Paste your numbers
Separated by spaces, commas, or new lines. Copying a spreadsheet column works.
- 2
Choose sample or population
Sample divides by n − 1 and is the right default for survey data. Population divides by n.
- 3
Read spread and center together
Standard deviation leads, with variance, mean, count, and range beside it.
Why use this standard deviation calculator
One number tells you how spread out your data is. Two averages can match while the experiences behind them look nothing alike.
Forgiving input
Commas, spaces, tabs, semicolons, and line breaks all separate values, so you can paste straight from a sheet.
Context around the number
A standard deviation of 4 means something different for a mean of 5 than for a mean of 500. The mean is right there.
When spread matters
Survey rating spread
See whether a 4.2 average came from consistent 4s or a split between 2s and 5s.
Quality and process checks
Track variability in delivery times, weights, or response times, not just the average.
Homework and lab reports
Check your working with both the sample and population formulas.
Sample and population formulas
s = √( Σ(xᵢ − x̄)² ÷ (n − 1) ) · σ = √( Σ(xᵢ − μ)² ÷ n )
The only difference is the denominator. Dividing by n − 1 (Bessel's correction) removes the bias you get when estimating spread for a wider population from a sample of it.
Reading a standard deviation
- For roughly normal data, about 68% of values sit within one standard deviation of the mean and about 95% within two.
- Compare spread across different scales by dividing by the mean (the coefficient of variation).
- A standard deviation of zero means every value is identical.
- Outliers move standard deviation much more than they move the median.
Related calculators
Frequently asked questions
How do you calculate standard deviation?
Find the mean, subtract it from every value, square each difference, average those squares, then take the square root.
The averaging step is where sample and population differ: a sample divides by n − 1, a population divides by n.
Should I use the sample or population formula?
Use sample (n − 1) when your numbers are a subset of a bigger group you want to describe, which covers almost every survey and experiment.
Use population (n) only when you have measured every member of the group, for example every employee in a 40-person company.
What is the difference between variance and standard deviation?
Variance is the average squared distance from the mean. Standard deviation is its square root.
Both measure the same thing, but standard deviation is in the original units, so it is the one you can quote next to the mean. This tool shows both.
What is a good standard deviation?
There is no universal target. It depends entirely on the scale and on how much variation is acceptable in your context.
Relative to the mean is the useful read: a standard deviation of 2 on a 1 to 5 rating scale is huge, while 2 on a 500ms response time is negligible.
Can standard deviation be negative?
No. It is a square root of an average of squares, so it is always zero or positive. Zero means every value in the list is the same.
How does this relate to z-scores?
A z-score is how many standard deviations a value sits from the mean. Get the mean and standard deviation here, then feed both into the z score calculator.
Is my data stored?
No. Parsing and calculation happen entirely in your browser.
Collecting fresh survey responses? Try Formms for a form with a short link and QR.
Collect the responses on your phone next.
Formms builds the survey from a prompt, then you can paste counts back into these calculators anytime.
View a demo form →