Standard Deviation Calculator
Find standard deviation, variance, and mean for a data set.
Paste a list of numbers to get the standard deviation — both population and sample — along with the variance, mean, and count. Standard deviation measures how spread out your data is around the average.
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📖 Read the guide: Standard Deviation Explained: What It Is and How to Calculate It
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Formula
Population standard deviation (σ)
√( Σ(x − mean)² ÷ N )
Use when your data is the entire population. Divides by N.
Sample standard deviation (s)
√( Σ(x − mean)² ÷ (N − 1) )
Use when your data is a sample of a larger population. Divides by N − 1 (Bessel's correction).
How to use the standard deviation calculator
- 1Enter your numbers separated by commas, spaces, or new lines.
- 2Read the sample and population standard deviation, variance, and mean.
- 3Copy the value you need (sample SD is the most common).
Examples
| Example | Input | Result |
|---|---|---|
| Tight spread | 5, 5, 6, 6 | σ ≈ 0.5 |
| Classic set | 2,4,4,4,5,5,7,9 | σ = 2 · s ≈ 2.14 |
| Wide spread | 1, 50, 100 | large σ |
Population vs. sample standard deviation
If your numbers represent the entire group you care about, use the population standard deviation (divide by N). If they're a sample drawn from a larger population and you're estimating the whole, use the sample standard deviation (divide by N − 1). The N − 1 correction makes the sample estimate less biased. In most real-world statistics — surveys, experiments, quality control — you have a sample, so the sample standard deviation is the usual choice.
What standard deviation tells you
Standard deviation is the typical distance of a value from the mean. A small standard deviation means the data clusters tightly around the average; a large one means it's spread out. Variance is simply the standard deviation squared — useful in further calculations but in squared units, which is why standard deviation (in the original units) is usually reported.
Frequently asked questions
What is standard deviation?
A measure of how spread out numbers are around their mean. Low means clustered; high means dispersed.
Should I use population or sample standard deviation?
Use population (÷N) if your data is the whole group; use sample (÷N−1) if it's a sample estimating a larger population. Sample is the common default.
What is the difference between variance and standard deviation?
Variance is the average squared distance from the mean; standard deviation is its square root, expressed in the original units.
Is my data private?
Yes. All statistics are computed in your browser and never uploaded.
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