Standard Deviation Calculator
Free, with no sign up. Calculations run on your device; your entries stay in this browser.
Sample and population standard deviations appear first. Use sample SD when describing a sample with the n − 1 denominator, and population SD for the complete list with the n denominator. Enter 1–1,000 values separated by commas, spaces or newlines, each between −1,000,000,000,000 and 1,000,000,000,000 (±10¹²). Optionally enter one weight per value, each from 0 to 1,000,000,000 (10⁹), with at least one positive weight. Values text is capped at 24,000 characters and weights at 14,000. Decimal and scientific notation are accepted. Values must share the same unit: mean, median, mode, range and standard deviation use that unit, sum uses its total, and count is unitless. Weights are relative, unitless amounts.
Your result
mean = Σx/n; weighted mean = Σ(wx)/Σw; population SD = √(Σ(x − mean)²/n); sample SD = √(Σ(x − mean)²/(n − 1)); median = middle sorted value or mean of the middle pair.
Primary source: OpenStax Introductory Statistics 2e, measures of center; OpenStax Introductory Statistics 2e, population and sample standard deviation.
All ordinary statistics use the unweighted list; optional weights affect only the separately labelled weighted average. Modes include every repeated value tied for highest frequency; if all values occur once, there is no mode. For a single value, population SD is zero and sample SD is undefined. Floating-point results display up to 12 significant digits and may be approximate.
Worked example
For 2, 4, 4, 6, sum = 16, count = 4, mean = 4, median = 4, mode = 4 and range = 4. Population SD = √2 ≈ 1.41421356237; sample SD = √(8/3) ≈ 1.63299316186. Weights 1, 1, 1, 3 give a weighted average of 28/6 ≈ 4.66666666667.
How to use this tool
Enter values separated by commas, spaces or newlines and select Calculate. Both sample and population SD appear first, followed by mean and count. Use the same unit for every value.
Frequently asked questions
How do sample and population SD differ?
Population SD divides the squared deviations by n. Sample SD divides them by n minus 1. Both use the unweighted mean of the entered list.
What happens with only one value?
Population SD is zero. Sample SD is undefined because its denominator is zero; at least two values are needed.
Do optional weights change either standard deviation?
No. Weights affect only the separate weighted average. Both standard deviations use the original unweighted list and retain the input unit.