BCBetter Calculators

Standard Deviation Calculator

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

🧮

Enter your values and click Calculate

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.

Related Calculators

life✨

Median

Find the median of up to 8 numbers.

Calculate →
life✨

Range

Calculate the statistical range (max minus min) for up to 8 numbers.

Calculate →
life✨

Mode

Find the most frequently occurring value in a set of up to 8 numbers.

Calculate →