Standard Deviation Calculator
Paste your data and get the population and sample standard deviation, variance and mean - every step shown.
Runs entirely on your device - nothing is ever uploaded.
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How to use the standard deviation calculator
- Enter at least two numbers, separated by spaces, commas or line breaks.
- Read the population and sample results side by side.
- Scroll the steps table to check each deviation, squared difference and the running sum.
Population vs sample: the N vs N-1 question
Population variance divides the squared differences by N, the number of values. Sample variance divides by N−1 (Bessel's correction), which compensates for the fact that a sample tends to underestimate the spread of the whole group. As a rule of thumb: describing the data you have means population; estimating something bigger from a sample means sample.
Worked example
For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5. The squared differences sum to 32. Population variance is 32 ÷ 8 = 4, so population standard deviation is 2. Sample variance is 32 ÷ 7 ≈ 4.571, giving a sample standard deviation of ≈ 2.138.