Standard Deviation Calculator
Calculate variance and standard deviation for a population or sample.
Result
Standard deviation: 2
Population divides by n; sample divides by n − 1.
- Variance
- 4
- Mean
- 5
- Sum of squared deviations
- 32
- Number of values
- 8
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Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the Standard Deviation Calculator
- Choose population when the entered values are the entire group, or sample when they are observations from a larger group.
- Enter one finite value per row; at least two rows are retained.
- Review the mean, variance and standard deviation together.
Population or sample is a real choice
First calculate the mean and each value’s squared distance from it. The divisor depends on what the entered list represents:
population variance = Σ(x − mean)² ÷ nsample variance = Σ(x − mean)² ÷ (n − 1)standard deviation = √varianceChoosing sample is not a way to obtain a preferred answer. It is appropriate only when the entered values are a sample used to estimate a larger population.
With your numbers
- Mean = 5; squared deviations total 32.
- Population variance = 4; standard deviation = 2.
Quick reference
Population divides by n; sample divides by n − 1.
| Example | Standard deviation |
|---|---|
| Population with standard deviation 2 | 2 |
| Sample 1 through 5 | 1.581139 |
| Equal population values | 0 |
| Two-value sample | 7.071068 |
| Decimal population | 0.816497 |
| Negative population | 1.632993 |
Common questions about the Standard Deviation Calculator
- What does standard deviation measure?
- It measures spread around the mean in the same units as the original values.
- What is the difference between population and sample?
- Population variance divides squared deviations by n. Sample variance divides by n minus 1 to estimate spread in a larger population.
- Why is variance in squared units?
- The formula squares each deviation before averaging. Standard deviation takes the square root to return to the original units.
- Can standard deviation be negative?
- No. Squared deviations and their square root cannot produce a negative value.