Standard Deviation Calculator
Paste a list of numbers to get the sample and population standard deviation, the variance, the mean and the sum of squared deviations, all at once. Values can be separated by commas, spaces or new lines. A free standard deviation calculator that runs in your browser.
- Exact, step-by-step answers
- 100% free
- No sign-up, no app
- Instant as you type
- Works offline after first load
Use the sample value (s) when your numbers are a sample of a larger group, and the population value (σ) when they are the whole group.
How to use it
- 1
Paste your numbers
Type or paste the data set into the box. Separate the values with commas, spaces or new lines, whichever is easiest.
- 2
Pick sample or population
Both are shown. Use sample when your numbers are drawn from a larger group, and population when they are the whole group.
- 3
Read the spread
See the standard deviation alongside the variance, mean and count, so you can tell how far the numbers sit from the average.
When it comes in handy
Statistics coursework
Get the variance and both standard deviations with the mean shown, so you can follow how each figure was reached.
Lab and test data
Measure how consistent a set of repeated readings is by checking how tightly they cluster around the mean.
Grades and results
See whether a set of scores is bunched together or widely spread, which the average alone does not tell you.
Instant, exact & 100% in your browser
The maths runs right here in your browser, with fractions and whole numbers kept exact rather than rounded along the way. Nothing you type is sent to a server, there is no sign-up and no limit, and once the page has loaded it keeps working even with no connection.
Frequently asked questions
- What is the difference between sample and population standard deviation?
- Population standard deviation divides by n, the count of values, and is right when your numbers are the entire group. Sample standard deviation divides by n − 1, which corrects for the fact that a sample tends to underestimate spread. The calculator shows both so you can use the one that matches your data.
- How is standard deviation calculated?
- Find the mean, subtract it from each value and square the result, average those squared differences to get the variance, then take the square root. The calculator shows the sum of squared deviations and the variance on the way to the answer.
- What is variance?
- Variance is the average of the squared differences from the mean, and the standard deviation is its square root. Variance is in squared units, while standard deviation is back in the original units, which is why it is usually the easier one to read.
- Does this work offline and is anything sent to a server?
- The calculation runs entirely in your browser, so nothing you type is sent anywhere, and once the page has loaded it keeps working with no connection. There is no sign-up and no limit on how many calculations you make.
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