Standard Deviation Calculator
Calculate sample or population standard deviation, variance, mean, median and quartiles from any list of numbers, with the working shown.
Sample standard deviation (s) —
- Count (n)
- —
- Sum
- —
- Mean
- —
- Variance (s²)
- —
- Median
- —
- Mode
- —
- Minimum
- —
- Maximum
- —
- Range
- —
- Q1 (25th pct)
- —
- Q3 (75th pct)
- —
- IQR
- —
- Sum of squares
- —
- Standard error
- —
- Coeff. of variation
- —
Working, step by step
Enter at least two numbers to see the calculation.
How it works
Paste your numbers separated by commas, spaces or new lines and every statistic updates as you type. The standard deviation is the square root of the variance: the tool subtracts the mean from each value, squares those deviations, adds them up, and divides that sum of squares by n − 1 for a sample or by n for a whole population — the Bessel correction that stops a sample from underestimating the spread of the population it came from. Pick the wrong divisor and your answer will be slightly too small, which is why the Sample / Population switch sits right next to the result.
Alongside the standard deviation you also get the variance, mean, median, mode, range, quartiles and interquartile range, the standard error of the mean (SD ÷ √n) and the coefficient of variation, plus the full working so you can check each step by hand or copy it into your homework. All of the maths runs in JavaScript inside your own browser: your data is never uploaded, there is no sign-up and there are no ads. Copy the summary, download it as a text file, or export a CSV with every value's deviation and squared deviation.
Frequently asked questions
What is the difference between sample and population standard deviation?
The only difference is the divisor. A population standard deviation divides the sum of squared deviations by n, because you have measured every member of the group. A sample standard deviation divides by n − 1 — the Bessel correction — because a sample's values cluster slightly closer to their own mean than to the true population mean, so dividing by n would systematically underestimate the spread. For 2, 4, 4, 4, 5, 5, 7, 9 the population SD is exactly 2 while the sample SD is 2.13809. Use the Sample / Population switch above the result to see both.
How do you calculate standard deviation by hand?
Add the numbers and divide by how many there are to get the mean. Subtract the mean from each value to get its deviation, square each deviation, and add the squares together — that total is the sum of squares. Divide it by n − 1 for a sample or by n for a population to get the variance, then take the square root for the standard deviation. The calculator prints all four steps with your actual numbers underneath the results, and the CSV export lists every value's deviation and squared deviation so you can check the arithmetic line by line.
Is my data uploaded anywhere?
No. Every calculation runs in JavaScript inside your own browser, so the numbers you paste are never sent to a server, logged or stored — the page keeps working with no connection once it has loaded. There is no account, no ads and no trackers, which makes it safe for lab measurements, grades, salary figures or any other data you would not want to paste into a hosted calculator.