What is Standard Deviation Calculator?

A standard deviation calculator measures how spread out numbers are in a data set. It computes both population and sample standard deviation along with mean, variance, and other descriptive statistics, so you can quickly assess data variability.

The calculator parses numbers from any layout — commas, spaces, line breaks, or a mix — so pasting a column out of Excel works without cleanup. It returns the mean, median, mode, variance, range, and sum, plus the coefficient of variation, quartiles (Q1, Q3) with the interquartile range, and skewness and excess kurtosis so you can judge the shape of the spread, not just its size. You can switch between population (σ, dividing by N) and sample (s, dividing by N-1) depending on whether your numbers represent the full group or a draw from a bigger one.

How to use

1. Enter your numbers separated by commas, spaces, or one per line in the input field.
2. Choose between population standard deviation (σ) for complete data sets or sample standard deviation (s) for data samples.
3. View the calculated mean, variance, standard deviation, and other statistics. Copy or download the results.

When to use

• Comparing exam, sales, or experiment results to see how consistent the values are.
• Checking quality-control measurements against a tolerance before reporting.
• Verifying a stats homework answer or a finance spreadsheet figure quickly.

Result

You have test scores: 85, 90, 78, 92, 88, 76, 95, 82. Enter these values, select sample standard deviation, and get s = 6.73 with a mean of 85.75, showing moderate score spread around the average.

FAQ

What's the difference between sample and population standard deviation?

Population (σ) uses every member of the group and divides by N. Sample (s) treats your numbers as a draw from a bigger group and divides by N-1, which corrects the bias that a small sample tends to understate spread.

How many data points do I need for the result to mean anything?

Sample standard deviation requires at least two points, but the figure stays jumpy until you reach roughly 20–30. For tight estimates of population spread aim for 30 or more, and report the count alongside the value.

What input formats does the calculator accept?

Numbers separated by commas, spaces, tabs, semicolons, or line breaks all work. Negative values, decimals, and scientific notation (1.2e-3) parse the same way. Non-numeric tokens are skipped, so stray labels won't break the result.

Why is my variance such a large number compared to the standard deviation?

Variance is the average of squared deviations, so its units are squared too (kg², dollars²). Standard deviation is the square root of variance, bringing the figure back to the original units, which is why it's easier to read.

Can I work out the standard deviation of percentages or ratios?

Yes, but treat the values as decimals (0.25, not 25%) for consistency. Standard deviation of percentages can be misleading when the underlying base values differ a lot — consider reporting the coefficient of variation alongside it.

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