Complete guide
Standard deviation calculator for sample and population data
Paste up to 1,000 values and choose population or sample. Calculator24 reports mean, variance, standard deviation, range and every squared deviation.
What standard deviation means
Standard deviation measures spread around the mean in the original units. Variance is its square and therefore uses squared units.
Population formula
When the list is the entire population, divide the squared-deviation sum by n.
σ=√(Σ(x−μ)²/n)Sample formula
For a sample estimating a larger population, divide by n−1. At least two values are required.
s=√(Σ(x−x̄)²/(n−1))Calculation steps
Find the mean, subtract it from each value, square the deviations, add them, divide by the selected denominator and take the square root.
Interpret spread carefully
Standard deviation uses every observation and can be sensitive to extreme values. Compare it only across compatible units and definitions.
Population versus sample
| Definition | Denominator | Minimum n |
|---|---|---|
| Population | n | 1 |
| Sample | n−1 | 2 |
Frequently asked questions
What is a low standard deviation?
It means values cluster more closely around their mean on that scale.
What is variance?
It is the mean squared deviation; standard deviation is its square root.
Should I choose sample or population?
Choose population for the complete group and sample when estimating a larger group.
Can standard deviation be negative?
No. Squares and the positive square root make it nonnegative.
Does this ignore duplicates?
No. Every entered observation is included.
What to keep in mind
Choose sample only when the entered observations are a sample used to estimate a larger population.
Results display up to 8 decimal places; exported numbers preserve calculation precision. This is a calculation summary, not an official certificate.