Standard Deviation Calculator

Calculate population and sample standard deviation for up to 8 values.

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Enter your values and click Calculate

Standard deviation measures how spread out values are around the mean. A low SD means values are clustered near the mean; a high SD means they are widely scattered. Use sample SD when your data is a subset of a larger population; use population SD when you have the full population. This calculator accepts up to eight values and displays both sample and population standard deviation simultaneously, along with their respective variances, the mean, and the count of values included. This makes it useful for quick statistical summaries in quality control, academic research, sports analysis, financial data review, and any scenario where understanding the variability of a small dataset matters. The distinction between sample and population SD — governed by whether you divide by n or n−1 — is often misunderstood, and showing both results side by side helps you choose the correct figure for your application without needing to recalculate.

How It Works

The calculator begins by computing the arithmetic mean of all active values: sum ÷ n. It then calculates each value's squared deviation from that mean — (value − mean)² — and sums all those squared deviations. For population standard deviation, the sum is divided by n (the full count) to produce population variance, and the square root gives the population SD (σ). For sample standard deviation, the sum is divided by n − 1 (Bessel's correction) to produce sample variance, and the square root gives the sample SD (s). Bessel's correction compensates for the tendency of a sample to underestimate the true population spread. Both variants are shown simultaneously so you can choose the one appropriate for your context. Mean, count, and both variance figures are also displayed for a complete statistical summary.

Examples

Values: 2, 4, 4, 4, 5, 5, 7, 9
Classic textbook dataset.
Result: Population SD = 2.0, Sample SD ≈ 2.14.
Consistent test scores
Values 85, 87, 86, 88, 85, 87.
Result: Mean 86.3, population SD ≈ 1.03 — tightly clustered scores.
Spread-out values
Values 10, 30, 50, 70, 90, 110.
Result: Mean 60, population SD ≈ 36.06 — high variability.

Frequently Asked Questions

Sample vs population SD — which should I use?
Use sample standard deviation (which divides by n−1) when your values are a sample drawn from a larger population and you want to estimate the true population spread. Use population standard deviation (which divides by n) when your data represents the entire population you care about — for example, all students in a single class.
What is variance?
Variance is the square of the standard deviation — it is the average of the squared differences from the mean. Variance is mathematically convenient for statistical formulas and proofs, but harder to interpret directly because its units are squared (e.g. dollars-squared). Standard deviation, being the square root of variance, brings the measure back to the same unit as the original data.
What does a standard deviation of zero mean?
A standard deviation of zero means every value in the dataset is identical — there is no spread or variability at all. This can be a useful validation check: if you expect variability in your data but get a zero SD, it likely indicates all inputs were accidentally set to the same value.

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