Standard Deviation Calculator
Sample and population standard deviation, variance and mean from any dataset.
The Standard Deviation Calculator returns sample and population standard deviation, variance, mean and count for any set of numbers — the toolkit for measuring how spread out data is.
Standard deviation answers 'how far from average are the values, typically': test scores clustering tightly around 75 have small σ, a dataset ranging from 40 to 110 has large σ. In a normal distribution, about 68% of values fall within ±1σ of the mean and 95% within ±2σ — the rule behind quality control, finance volatility and grading curves.
Two versions are shown because they answer different questions: sample standard deviation (dividing by n−1) estimates the population from a sample; population standard deviation (dividing by n) describes a complete dataset. Runs locally in your browser.
Sample σ
3.1623
n − 1 (use for samples)
Population σ
2.9277
÷ n (whole population)
Variance (sample)
10.0000
Mean
15.0000
7 values
Standard deviation measures spread: about 68% of values fall within ±1σ of the mean in a normal distribution, 95% within ±2σ.
How to use the Standard Deviation Calculator
- Enter your numbers (comma, space or newline separated).
- Read the sample standard deviation (n−1) for sampled data.
- Read the population standard deviation (n) for complete data.
- Check variance and mean alongside.
- Compare datasets to see which is more consistent.
Frequently asked questions
What is the difference between sample and population standard deviation?
Population σ divides by n and describes an entire dataset. Sample σ divides by n−1 (Bessel's correction) to avoid underestimating spread when you only measured a sample — use it unless your data covers everything.
How do I interpret a standard deviation?
It is the typical distance from the mean. Low σ = consistent values; high σ = wide spread. For roughly normal data, 68% sits within ±1σ and 95% within ±2σ of the mean.
Is variance the same as standard deviation?
Variance is σ² — the average squared deviation. Standard deviation is its square root, which returns to the original units, making it the figure people actually read and compare.
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