Standard deviation calculator for sample and population data
Paste up to 1,000 values and choose population or sample. HitEquals reports mean, variance, standard deviation, range and every squared deviation.
Inputs used by this calculator
Standard Deviation Calculator uses the fields below. The starting values reproduce the page example; replace them with values from the same units and time period before using the result.
| Input | Starting example | Accepted value | How it is used |
|---|---|---|---|
| Data values | 2, 4, 4, 4, 5, 5, 7, 9 | Text or a list in the format shown | Supplies the data values quantity used by the published equation or result breakdown. |
| Data definition | Population — divide by n | Population — divide by n · Sample — divide by n−1 | Chooses which Standard Deviation Calculator method or unknown the engine evaluates. |
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.
What the Standard Deviation Calculator answers
Calculate sample or population variance and standard deviation from raw data.
Use Standard Deviation Calculator when you know Data values and Data definition and need the relationship expressed by the published equation.
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 question does this Standard Deviation Calculator answer?
Calculate sample or population variance and standard deviation from raw data.
What to keep in mind
Choose sample only when the entered observations are a sample used to estimate a larger population.
Results are rounded for display in US format, with money in dollars and cents; CSV exports keep full calculation precision. This is a calculation summary, not an official certificate.