Standard Deviation Calculator – Sample & Population
Population and sample standard deviation, variance and mean.
About the Standard Deviation Calculator
What is the Standard Deviation Calculator?
A standard deviation calculator measures how spread out a dataset is from its mean, for both samples and populations.
Why use this calculator?
Standard deviation is the language of quality control, finance risk and test scoring — any time you need "how much values vary".
How to use it
- Enter numbers separated by commas.
- Choose sample or population data.
- Read the standard deviation, variance and mean.
Formula
SD = √( Σ(x−μ)² ÷ (n−1) ) for samples, ÷ n for population.
Sample mode applies Bessel\u2019s correction so the estimate is unbiased for the underlying population.
Frequently Asked Questions
What does "68-95-99.7" mean?
In a normal distribution, 68% of data lies within 1 SD of the mean, 95% within 2, 99.7% within 3.
Sample or population — which do I pick?
Population if you have every value; sample if you only have a subset and are estimating the whole.
What order of operations does this use?
It follows standard PEMDAS/BODMAS rules: parentheses, exponents, multiplication and division, then addition and subtraction.
How precise are the answers?
The calculator uses double-precision floating-point math (about 15 significant digits) and rounds the display. For exact symbolic results use dedicated algebra software.
Can I enter negative numbers or decimals?
Yes. Negative values, decimals and very large or small numbers are all supported unless a field says otherwise.
What does it mean if I get an error?
Errors usually mean an invalid input, such as division by zero or a negative value where only positives make sense. Check your entries and try again.
What is the difference between population and sample?
A population includes every member of a group; a sample is a subset. Sample statistics use n−1 in the denominator to correct for bias.
When should I use median instead of mean?
Use the median when data contains outliers or is skewed, because it is less affected by extreme values than the mean.
What does standard deviation tell me?
It measures how spread out the values are around the mean. A small standard deviation means the data clusters tightly; a large one means it is more scattered.
Is this calculator free to use?
Yes. Every calculator on this site is completely free, with no hidden fees, no subscriptions and no limits on how many times you can use it.