Sample Standard Deviation Calculator
Find the sample standard deviation (s) of your data with the n − 1 formula, plus variance, mean, standard error and a step-by-step deviation table.
The sample standard deviation, written s, measures how spread out your measurements are when they are a sample from a larger group. It divides by n − 1 instead of n (Bessel’s correction), which makes the sample variance an unbiased estimator of population variance; the square root itself is still slightly biased. Paste your numbers to get s, the sample variance, the mean and a row-by-row table you can check by hand.
How to use this tool
- Type or paste your values, separated by commas, spaces or line breaks.
- Read the sample standard deviation s, with the sample variance and the mean beneath it.
- Use the table to follow each value’s deviation from the mean and its square.
- If the numbers cover the entire population, use the population standard deviation (σ) listed further down.
Formula
s = √[ Σ(xᵢ − x̄)² ÷ (n − 1) ]
xᵢ is each value, x̄ is the mean and n is the number of values. Σ(xᵢ − x̄)² is the sum of squared deviations. The standard error of the mean is s ÷ √n and the coefficient of variation is s ÷ |x̄| × 100%.
Example
Eight commute times in minutes: 24, 31, 18, 27, 35, 22, 29, 30. They total 216, so the mean is 216 ÷ 8 = 27. The deviations are −3, 4, −9, 0, 8, −5, 2 and 3, and their squares add to 9 + 16 + 81 + 0 + 64 + 25 + 4 + 9 = 208. Dividing by n − 1 = 7 gives a sample variance of 29.714286, so s ≈ 5.451081 minutes. Dividing by 8 instead would give the population figure σ ≈ 5.09902.
Frequently asked questions
When should I use the sample rather than the population standard deviation?
Use the sample version whenever your numbers are a subset used to say something about a bigger group: survey answers, a few production batches, last month’s daily sales. Use the population version only when you have every member of the group you are describing.
Why divide by n − 1?
Deviations are measured from the sample’s own mean, which sits closer to the sample values than the true population mean does. That makes the squared deviations slightly too small on average; dividing by n − 1 corrects the variance so it is an unbiased estimate.
Is this the same as STDEV.S in Excel?
Yes. Excel’s STDEV.S and Google Sheets’ STDEV use the same n − 1 formula. STDEV.P gives the population figure.
Why does one value give an error?
With n = 1 the divisor n − 1 is zero, so s is undefined. You need at least two values.
Last updated: 2026-10-30