About the Variance Calculator
What is the Variance Calculator?
Variance is the average of the squared distances of each value from the mean. Squaring makes every deviation positive and gives extra weight to values far from the mean. It is the foundation of standard deviation, ANOVA, regression and portfolio risk calculations.
Enter your data and choose sample or population. The calculator shows every step: the mean, the sum of squared deviations, the variance and its square root, the standard deviation.
How to use the Variance Calculator
- Data Values (separated by commas or spaces) — separate numbers with commas, spaces or line breaks. (sample: 10, 12, 23, 23, 16, 23, 21, 16)
- Data Type (sample: Sample (s², divide by n − 1))
- Press Calculate Variance (results also refresh as you type). The result card shows the Variance, along with Standard deviation, Mean, Sum of squared deviations and Count.
Formula used
s² = Σ(x − x̄)² ÷ (n − 1) σ² = Σ(x − μ)² ÷ N
- x̄, μ = the sample or population mean
- Σ(x − x̄)² = the sum of squared deviations
- n − 1 = degrees of freedom for a sample
Dividing by n − 1 for a sample corrects for the fact that a sample's own mean is used, which would otherwise make the spread look slightly too small.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| Data Values (separated by commas or spaces) | 10, 12, 23, 23, 16, 23, 21, 16 |
| Data Type | Sample (s², divide by n − 1) |
| Result | Value |
|---|---|
| Variance | 27.4286 |
| Standard deviation | 5.2372 |
| Mean | 18 |
| Sum of squared deviations | 192 |
| Count | 8 |
Tips for using the Variance Calculator
- Variance is in squared units (for example ₹² or cm²); take the square root to get back to the original units.
- Adding the same constant to every value does not change the variance; multiplying every value by k multiplies the variance by k².
- For two independent variables, the variance of their sum is the sum of their variances.