Variance Calculator
Variance measures how spread out data is from the mean. This calculator computes both population variance (dividing by N) and sample variance (dividing by N-1). Enter a comma-separated list of numbers, and the calculator displays population variance, sample variance, and related statistics. Sample variance uses Bessel's correction (N-1) to provide an unbiased estimate of population variance when analyzing a sample. Variance is fundamental to statistics, quality control, finance, and risk analysis.
Variance formulas
mean = sum of values / N
Population variance (σ²) = sum of (x - mean)² / N
Sample variance (s²) = sum of (x - mean)² / (N - 1)
Relationship to standard deviation
- Population standard deviation (σ) = sqrt(σ²)
- Sample standard deviation (s) = sqrt(s²)
- Standard deviation is more interpretable because it is in the same units as the original data
Variance calculator: frequently asked questions
What is variance?
Variance measures how spread out data is from the mean. It is the average of the squared deviations from the mean. Population variance divides by N; sample variance divides by (N-1). Variance is in squared units, making it less intuitive than standard deviation (which is the square root of variance).
What is the difference between variance and standard deviation?
Standard deviation is the square root of variance. Both measure spread, but standard deviation is in the same units as the original data, making it more interpretable. Variance is more useful mathematically and in statistical formulas.
Why divide by (N-1) for sample variance?
Dividing by (N-1) instead of N is called Bessel's correction. It corrects the bias that occurs when estimating population variance from a sample. Sample variance (dividing by N-1) is an unbiased estimator of population variance, while dividing by N tends to underestimate.
When should I use population vs. sample variance?
Use population variance when you have data for an entire population. Use sample variance when analyzing a sample from a larger population (the typical case). Sample variance is slightly larger due to Bessel's correction.
What is a high variance?
High variance means data is widely spread from the mean. Low variance means data clusters closely around the mean. A variance of 0 means all data values are identical.
Official sources
- Statistical definitions: National Institute of Standards and Technology.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.