Measure how spread out values are around the mean with variance and standard deviation.
Overview
Standard deviation quantifies spread around the average. Two datasets can share the same mean yet feel very different: one tightly clustered and one widely scattered. Variance and standard deviation capture that difference in one number.
Population standard deviation divides by N when your list is the entire group you care about. Sample standard deviation divides by n - 1 (Bessel correction) when the list is a sample meant to estimate a larger population. Pick the version that matches your statistical question.
This calculator computes the mean first, then sums squared deviations, then takes the square root for standard deviation. Squaring deviations prevents positive and negative gaps from canceling, which is why spread measures use squared error before the root step.
In practice, standard deviation helps compare volatility of investments, consistency of manufacturing parts, and variability of test scores. Always report whether you used population or sample formulas when sharing results.
Steps
Paste or type the full number list.
Select sigma (population) or s (sample) mode.
Review the average used as the center point.
See average squared deviation from the mean.
Use the square root of variance as spread in original units.
Run another list to contrast variability.
Math
sigma = sqrt(sum((xi - mu)^2) / N); s = sqrt(sum((xi - xbar)^2) / (n-1))
Subtract the mean from each value, square the differences, average them (with N or n-1), then take the square root to return to original units.
Worked cases
Mean=5; variance=4; sigma=sqrt(4)
Population standard deviation = 2.
Divide sum of squared deviations by 7 instead of 8
Sample standard deviation ≈ 2.138.
Same mean possible, different squared deviations
Set B has much larger standard deviation.
Why use this
Questions