Standard deviation measures how spread out a set of numbers is: how far, on average, values sit from the mean. A small standard deviation means the data clusters tightly, and a large one means it's widely scattered. It's a cornerstone of statistics homework, lab reports, quality control, finance (where it measures volatility) and grading curves. Calculating it by hand is tedious and error-prone. This free standard deviation calculator takes any list of numbers, separated by commas, spaces, tabs or new lines (so you can paste straight from a spreadsheet column), and instantly returns both the sample standard deviation (dividing by n − 1, used when your data is a sample from a larger group) and the population standard deviation (dividing by n, used when you have every value), along with both variances. You also get the full set of descriptive statistics: count, sum, mean, median, mode (including multiple modes), minimum, maximum, range, quartiles (Q1, Q3) and interquartile range, the standard error of the mean, and the coefficient of variation. A step-by-step table shows each value's deviation from the mean and its square, exactly as you'd lay it out on paper, and a simple dot plot shows the distribution. Calculations run in your browser with a numerically stable method.
Calculate
Step-by-step working
Formulas
- Mean: x̄ = Σx ÷ n
- Sample variance: s² = Σ(x − x̄)² ÷ (n − 1)
- Population variance: σ² = Σ(x − μ)² ÷ n
- Standard deviation = √variance
Sample or population?
Use sample when your numbers are a subset (a survey, a test batch). Use population only when you have every member of the group.
FAQ
Why are there two standard deviations?
Sample SD divides by n − 1 to correct for bias when estimating from a sample; population SD divides by n.
How are quartiles calculated?
Using the common “median of halves” method (excluding the median for odd n). Other software may use slightly different methods.
Can I paste from Excel or Google Sheets?
Yes. Copy a column and paste; new lines and tabs are fine.
Is my data uploaded?
No. Everything runs in your browser.
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