Standard Deviation Calculator

Calculate population or sample standard deviation from numbers pasted with commas, spaces, tabs or new lines. See count, sum, mean, median, minimum, maximum, range and variance with a formula breakdown, and download CSV or text.

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About the Standard Deviation Calculator

Standard Deviation Calculator measures how spread out a set of numbers is. Paste or type values separated by commas, spaces, tabs or new lines — straight from a spreadsheet column, for example — and choose population standard deviation (σ, dividing by N) or sample standard deviation (s, dividing by n − 1). The tool shows the count, sum, mean, median, minimum, maximum, range, variance and standard deviation.

A formula breakdown uses your actual values, showing the mean, the sum of squared deviations, the variance and the square root. Calculations use a two-pass method with compensated summation for accuracy, results are displayed to 12 significant digits, and the CSV download keeps full double-precision values together with each value’s deviation. Invalid entries such as text, NaN or infinite values are listed by position, and up to 100,000 values are supported.

How to use

Paste or type your numbers into the box.
Choose Sample or Population standard deviation.
Click Calculate.
Read the statistics and the formula breakdown.
Copy the summary or download it as text or CSV.

Key features

Accepts commas, spaces, tabs and new lines.
Sample (n − 1) and population (N) modes.
Count, sum, mean, median, min, max, range, variance and SD.
Formula breakdown with your values.
CSV with full-precision values and deviations, plus text summary.
Up to 100,000 values, clear error messages and full Reset.

Best practices

Use sample SD when your data is a sample of a larger group.
Use population SD only when you have every member of the group.
Check for typing errors — one outlier can change the SD a lot.
Keep units consistent across all values.
Report the mean together with the standard deviation.

Benefits

Quick, accurate statistics without a spreadsheet.
Transparent working for study and reports.
Handles large pasted datasets.
Private: your data never leaves the browser.

Frequently asked questions

What is the difference between sample and population standard deviation?

Population SD divides the sum of squared deviations by N, the number of values. Sample SD divides by n − 1, which corrects the bias when estimating a larger population from a sample.

Which one should I use?

Use sample SD when your values are a subset of a larger group (most surveys and experiments). Use population SD when the values are the entire group you care about.

What is variance?

Variance is the average squared deviation from the mean (dividing by N or n − 1). The standard deviation is its square root, in the same units as the data.

What input formats are accepted?

Numbers separated by commas, spaces, tabs or new lines, including negatives, decimals with a dot and scientific notation such as 1.5e3. Text, NaN and Infinity are rejected with their position.

Why does sample mode need two values?

It divides by n − 1, which is zero for a single value, so the sample standard deviation is not defined for one number.

How many values can I enter?

Up to 100,000 values. Larger lists are rejected with a message so the page stays responsive.

Is my data saved or uploaded?

No. Every calculation runs in your browser. Nothing you type is sent to a server or saved in browser storage, and Reset clears it from the page.