Standard Deviation Calculator
Sample & population SD, variance & mean.
100% private — runs in your browser, nothing is uploaded.
Sample standard deviation (s)
2.13809
Population standard deviation (σ)
2
Sample variance (s²)
4.571429
Population variance (σ²)
4
Mean (x̄)
5
Count (n)
8
Sum of squared deviations: 32 — sample formulas divide by n−1 (7), population by n (8).
Everything is calculated locally in your browser — your data never leaves your device.
How to use the Standard Deviation Calculator
- 1Paste your data
Separate values with commas, spaces or new lines.
- 2Pick the right figure
Sample (s) for samples, population (σ) for full groups.
- 3Check variance and mean
Both variances and the mean are shown alongside.
- 4Verify the working
The sum of squared deviations is displayed for checking homework.
Examples
| Input | Output |
|---|---|
2, 4, 4, 4, 5, 5, 7, 9 | σ = 2 · s ≈ 2.13809 |
10, 10, 10 | σ = 0 (no spread) |
Sample and population standard deviation, together
This standard deviation calculator takes any list of numbers and instantly returns both the sample standard deviation (s, dividing by n−1) and the population standard deviation (σ, dividing by n), along with both variances, the mean and the count. Showing both versions side by side removes the most common source of wrong answers in statistics homework.
What the number actually tells you
The mean says where your data centers; the standard deviation says how far values typically stray from it. Two classes can both average 70% while one is full of 65–75s and the other swings from 40 to 100 — the standard deviation is the number that separates those stories. In roughly normal data, about 68% of values fall within one standard deviation of the mean and 95% within two.
Built for checking work
The tool also displays the sum of squared deviations — the intermediate value most textbooks make you compute — so you can find exactly where a manual calculation went wrong. Start with the average calculator if you only need central measures, and paste data straight from a spreadsheet: commas, spaces and new lines all work.
Frequently Asked Questions
What is standard deviation?
A measure of how spread out numbers are around their mean. A small standard deviation means values cluster tightly; a large one means they vary widely. It's expressed in the same units as the data.
Sample vs population standard deviation — which should I use?
Use the population formula (divide by n) only when your data is the entire group. If your data is a sample used to estimate a larger group — the usual case — use the sample formula (divide by n−1). This tool shows both.
Why divide by n−1 for a sample?
It's Bessel's correction. A sample's spread around its own mean slightly underestimates the true population spread, and dividing by n−1 instead of n corrects that bias on average.
What is variance?
Variance is the average of squared deviations from the mean — the standard deviation squared. It's mathematically convenient but in squared units, which is why the standard deviation is usually reported.
How is standard deviation calculated step by step?
1) Find the mean. 2) Subtract the mean from each value and square the result. 3) Sum those squares. 4) Divide by n (population) or n−1 (sample). 5) Take the square root.
Is my data private?
Yes — all statistics run locally in your browser. Nothing you paste is uploaded.