Compute sample or population standard deviation, variance, mean, and range for any data set.
Sample standard deviation (n − 1 divisor, Bessel's correction) for small data sets. Use the calculator above for arbitrary datasets and the full breakdown:
| Data set | Values | Mean | Sample σ (n−1) | Population σ (n) |
|---|---|---|---|---|
| Constant series | 5, 5, 5, 5, 5 | 5.0 | 0.00 | 0.00 |
| Class scores | 85, 90, 78, 92, 88, 76, 95 | 86.3 | 7.04 | 6.51 |
| Stock returns (%) | 2.3, −1.5, 4.1, −0.8, 3.2, 1.8, −2.1, 5.5 | 1.56 | 2.71 | 2.53 |
| Body temperature (°F) | 98.6, 98.4, 99.1, 98.2, 99.0, 98.8 | 98.68 | 0.34 | 0.31 |
| Daily steps (thousands) | 4.2, 7.8, 9.5, 3.1, 12.0, 6.4, 8.7 | 7.39 | 3.16 | 2.93 |
Rule of thumb: use the n−1 (sample) divisor when your data is a subset of a larger population (most real-world use). Use the n (population) divisor only when your data set is the entire population. Reference: NIST/SEMATECH e-Handbook §1.3.3.
Use when your data is a sample of a larger population. Divides by n-1 (Bessel's correction) to give an unbiased estimate.
s = √[Σ(xᵢ - x̄)² / (n - 1)]
Use when your data represents the entire population. Divides by N.
σ = √[Σ(xᵢ - μ)² / N]
Type your numbers separated by commas or newlines. The calculator accepts any size data set from a few points to thousands.
Select Sample (when your data is a subset of a larger population) or Population (when you have all values). The formulas differ slightly.
Get the mean, variance, standard deviation, range, and a histogram. Standard deviation tells you the typical spread of values from the mean.
For related calculations, try our percentage calculator.
Cross-checked against authoritative formulas (IRS, NIST, ACSM) and updated for 2025/2026 tax years and rates.
No server roundtrip. All math runs in your browser so results appear the moment you finish typing.
We never collect, store, or transmit your inputs. Every calculation runs locally in your browser.
Each calculator includes the formula, plain-English explanation, and FAQs so you understand the result.
Estimates only. Calculator results are for educational and planning purposes — not professional advice. For binding decisions on taxes, investments, health, or legal matters, consult a qualified professional.