Standard Deviation Calculator
Paste a list of numbers to get the standard deviation, variance, mean, count, and sum, with the method shown.
Everything is calculated in your browser. Nothing is uploaded.
Data set
The squared differences from the mean are added up, then divided by n minus 1 (Bessel’s correction) because these numbers are treated as a sample of a larger group. The standard deviation is the square root of that variance.
- Sum of squared deviations
- 208.8333
- Divided by (n - 1)
- 5
- Variance
- 41.7667
- Standard deviation (square root of variance)
- 6.4627
How to calculate standard deviation
Enter your numbers
Paste or type your data set into the box, separated by commas, spaces, or new lines.
Choose sample or population
Pick sample if the numbers are a subset of a larger group, or population if they are the entire group.
Read the results
The standard deviation, variance, mean, count, and sum appear instantly and update as you edit.
Copy the summary
Use the copy button to grab every statistic as a plain-text summary for a report or spreadsheet.
Why use this tool
Sample and population both covered
A single toggle switches between dividing by n minus 1 for a sample and by n for a whole population, and every statistic recalculates at once.
Five statistics at a glance
Standard deviation, variance, mean, count, and sum are shown together, so you never have to run a second calculation to get the number you actually needed.
The method is shown, not hidden
A short breakdown lists the sum of squared deviations, the divisor used, the variance, and the square root that produces the standard deviation.
Forgiving input parsing
Commas, spaces, tabs, and line breaks all work as separators, and anything that is not a number is skipped and counted rather than breaking the result.
Runs entirely in your browser
Everything is calculated on your device as you type. Nothing is uploaded, stored, or logged.
About this tool
Standard deviation measures how spread out a set of numbers is around their mean. A small value means the numbers cluster tightly near the average; a large value means they are scattered widely. This calculator takes a list of numbers and reports the standard deviation, the variance it comes from, the mean, the count, and the sum together, so you can read the spread and the center of your data in one place instead of stitching results from several tools.
The choice between sample and population is the one that trips people up. Use population when your numbers are the entire group you care about, which divides the squared deviations by n. Use sample when your numbers are a subset meant to represent a larger group, which divides by n minus 1 to correct the bias that a sample introduces. This is the difference between the sigma and s notation you see in textbooks. The calculator makes the switch a single toggle and shows the divisor it used, so the result is never a mystery number.
Input parsing is deliberately forgiving: separate values with commas, spaces, tabs, or new lines, mix them freely, and paste a column straight from a spreadsheet. Negative numbers, decimals, and scientific notation are all accepted, and any entry that is not a number is skipped and counted so a stray label will not break the total. Everything runs in your browser as you type and nothing is uploaded. For related summaries, the percentage calculator handles one-off percentage changes, and the word frequency tool counts how often each item appears in a list.
Frequently asked questions
- What is the difference between sample and population standard deviation?
- Population divides the sum of squared deviations by n, the full count, and is used when your numbers are the entire group. Sample divides by n minus 1, which corrects the bias when your numbers are a subset drawn from a larger group. Sample values are always slightly larger. The toggle switches between them and shows the divisor used.
- How does the calculator read my numbers?
- Split your values with commas, spaces, tabs, or new lines in any combination. Decimals, negative numbers, and scientific notation all work. Anything that is not a valid number is skipped and reported as a count, so a stray heading or blank line will not throw off the result.
- Why do I need at least two numbers for a sample?
- Sample standard deviation divides by n minus 1, so a single value would divide by zero and has no defined spread. Population standard deviation of one value is defined and equal to zero. Add a second number or switch to population if you only have one value.
- What is variance and how does it relate to standard deviation?
- Variance is the average of the squared differences from the mean, using the sample or population divisor. Standard deviation is simply the square root of the variance, which brings the figure back into the same units as your original numbers.
- Is my data uploaded anywhere?
- No. Every calculation runs in your browser as you type. Your numbers are never sent to a server, stored, or logged.
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