Standard Deviation — Sample & Population, With Steps
Mean, variance and sample/population standard deviation with the full working shown. Client-side and private.
Show working (deviations from the mean)
| x | x − x̄ | (x − x̄)² |
|---|---|---|
Enter at least one number.
How to use
- 1 Paste or type your numbers, separated by commas, spaces or new lines.
- 2 Choose Sample (÷ n−1) or Population (÷ n).
- 3 Read the mean, variance and standard deviation — expand “Show working” for the steps.
Why use this tool
- Both sample and population standard deviation, switchable in one click.
- Shows every deviation and squared deviation so you can follow the maths.
- Runs entirely in your browser — your data never leaves the page.
Frequently asked questions
What is the difference between sample and population SD?
Population SD divides the sum of squared deviations by n; sample SD divides by n−1 (Bessel’s correction) to better estimate the spread of a wider population from a sample.
Which one should I use?
Use sample (s) when your numbers are a sample drawn from a larger group, and population (σ) when they are the entire group.
What is variance?
Variance is the average of the squared deviations from the mean; standard deviation is its square root, back in the original units.
What is the coefficient of variation?
The standard deviation expressed as a percentage of the mean — useful for comparing the relative spread of different datasets.
What is Standard Deviation Calculator?
A standard deviation calculator measures how spread out a set of numbers is, reporting the mean, variance and standard deviation for either a sample or a whole population.
Features
Sample or population
Sample SD uses n−1 (Bessel's correction); population SD uses n — toggle between them.
Mean, variance & SD
Reports the mean, sum of squares, variance, and standard deviation together.
Free & private
Runs on your device — your data is never uploaded.
Example
Input
2, 4, 6 (sample)Output
mean = 4 · sample SD (n−1) = 2Common use cases
-
1
Analyze measurements
Quantify the spread of a set of experimental or survey values.
-
2
Grades & scores
See how tightly scores cluster around the average.
-
3
Quality & finance
Measure variability in process outputs or returns.
Zerethon's standard deviation calculator computes the mean, variance, and standard deviation of a data set in your browser. It defaults to the sample standard deviation (dividing by n−1, Bessel's correction) and can switch to the population form (dividing by n). Everything runs client-side — nothing is uploaded.
- Category
- Math
- Pricing
- Free
- Privacy
- Browser-based
- Signup
- Not required
References
- Standard Deviation — Wolfram MathWorld — Wolfram MathWorld
- Bessel's correction (n−1) — Wikipedia
Privacy
Your data never leaves your browser unless explicitly stated. Standard Deviation Calculator runs entirely client-side — no server upload, no logging, no tracking of your input.
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