Variance Calculator
Paste or type a dataset to calculate sample and population variance side by side, then compare the corresponding standard deviation and mean.
Compare sample and population variance
Enter your values, or try an example.
Your results and calculation will appear here.
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How to use this calculator
- Enter your dataset. Repeated values are separate observations.
- Calculate to compare sample and population variance.
- Open calculation steps to see the mean, squared-deviation sum and divisors.
Worked example: small dataset
data: 1, 2, 3, 4, 5
Sample variance = 2.5; Population variance = 2
Sample variance is 2.5 squared units. Its square root is a sample SD of 1.5811 units.
Example calculation
- n = 5; sum = 15; mean = sum / n = 3.
- Squared-deviation sum Σ(x − mean)² = 10.
- Population variance = 10 / 5 = 2; population SD = √variance = 1.4142.
- Sample variance = 10 / 4 = 2.5; sample SD = 1.5811.
Formula & assumptions
Population variance = Σ(xᵢ − x̄)² / n; sample variance = Σ(xᵢ − x̄)² / (n − 1).
- Observations have equal weight.
- Sample variance requires at least two observations.
- Variance is expressed in squared units, not the original measurement units.
Variance vs. Standard Deviation
Variance measures the average squared deviation from the mean, while standard deviation is the square root of variance. Sample variance uses n − 1 in the denominator, whereas population variance uses N. Both describe variability, but standard deviation is expressed in the original units of the data.
For example, if a population has a variance of 25 square units, its standard deviation is 5 original units. Variance is useful for mathematical calculations, while standard deviation is often easier to interpret because it uses the same measurement units as the observations.
Standard deviation = √Variance
To calculate and compare both measures directly, use our Standard Deviation Calculator.
Sources
Reviewed: October 2026
Common questions
Why are variance units squared?
The calculation squares every deviation from the mean. Taking the square root gives standard deviation in the original units.
Use these tools for mathematical information, not as a substitute for checking assumptions. Read our methodology or disclaimer.