Standard Deviation From Variance
Calculator
Results
- Standard deviation
- 4.159326
Statistical results
| Standard deviation | 4.159326 |
formula-map diagram
- Standard deviation
- 4.159326
Statistical relationship
Formula
σ = √(σ²)= 4.1593268686171
Note
This is a simplified model: it applies the displayed standard formula to the summary values you entered and assumes their underlying conditions (independence, normality, correct sampling) hold. It does not analyse a real data set. Check the assumptions before relying on the result.
More in Statistics and probability
See all →Frequently asked questions
What is the relationship between variance and standard deviation?+
Standard deviation is the square root of variance. Variance is expressed in squared units of the original data, while standard deviation is back in the original units, which is why it's easier to interpret directly.
Why take the square root instead of just using variance?+
Squaring the deviations during variance calculation removes negative signs but also inflates the scale and changes the units. Taking the square root undoes that inflation and returns a number you can compare directly to your data's mean.
Can variance ever be negative?+
No, variance is always zero or positive because it's built from squared deviations. If you enter a negative number, there's no real standard deviation, which is a sign the variance value itself was miscalculated or mistyped.
What does a standard deviation of zero mean?+
It means every value in the data set is identical to the mean, so there's no spread at all. Any variance greater than zero always produces a positive standard deviation.
Is this the population or sample standard deviation?+
The square root operation is identical either way; what differs is how the variance itself was computed upstream (dividing by n for a population or n-1 for a sample). This calculator just converts whatever variance you supply, so make sure that variance matches the type of standard deviation you need.