Paste numbers separated by commas, spaces, or new lines. Toggle decimal comma if needed.
This free Variance Calculator lets you quickly compute the mean, population variance (σ²), sample variance (s²), and standard deviation of a dataset. Simply paste your numbers separated by commas, spaces, or new lines, and get instant results with a detailed step-by-step breakdown.
In statistics, variance measures how spread out a dataset is compared to its mean. It’s the average of the squared differences from the mean.
A small variance means data points are close to the mean.
A large variance means data points are more spread out.
Variance is expressed in squared units (e.g., cm², sec², $²).
$$ \sigma^2 = \frac{\sum (x_i - \mu)^2}{N} $$
$$ s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1} $$
Enter or paste your dataset into the input box.
Choose whether to use decimal point or decimal comma.
Click Calculate.
View results including:
Dataset: 12, 15, 18, 20, 21
So, the population variance = 10.96 and the sample variance = 13.7.
For example:
If variance = 9 (cm²), then standard deviation = 3 (cm).
Finance: measuring stock volatility and risk.
Science & Research: comparing variability in experiments.
Quality control: detecting inconsistent production.
Sports analytics: measuring performance variability.
Education: analysing spread of test scores.
Q: Why divide by n−1 in sample variance?
A: It corrects bias when estimating population variance from a sample (Bessel’s correction).
Q: Can variance be negative?
A: No. Since it’s based on squared deviations, variance is always ≥ 0.
Q: What’s the main difference between variance and standard deviation?
A: Variance is in squared units, while standard deviation is the square root of variance (same units as the data).
Q: When should I use population vs sample variance?
A: Use population variance if you have the full dataset; use sample variance if working with a subset.