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Free online variance calculator to quickly find sample variance, population variance, standard deviation, and mean. Easily evaluate data volatility and dispersion.
Enter at least 2 numbers. Supports separation by commas, spaces, newlines, or semicolons. Non-numeric input will be ignored.
Enter at least 2 numbers to calculate variance.
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
Variance summarizes how far a set of numeric observations spreads around its mean. For each value, subtract the mean, square that difference, add the squared differences, and divide by a denominator chosen for the question. Squaring gives larger departures more influence: a point 10 units from the mean contributes 100 squared units, while a point 2 units away contributes 4. The result is always nonnegative for ordinary finite inputs, and it is zero when all included values are equal.
Sum of squared deviations: SS = Σ(xᵢ − x̄)²
Sample variance: s² = SS / (n − 1)
Population variance: σ² = SS / n
Standard deviation: square root of the corresponding variance
Use population variance when the values are the complete group you want to describe. Use sample variance when the observations are a sample used to estimate variability in a larger population; the n − 1 denominator is the conventional unbiased estimator of population variance under the usual sampling assumptions. The calculator displays both results together, so you do not need to select a mode. NIST describes variance as squared distance from the mean and standard deviation as its square root, which returns the spread to the original measurement units. NIST’s discussion of measures of scale also explains why unusually distant observations can have a large effect.
Variance has squared units: measurements in inches produce variance in square inches, and scores measured in points produce variance in points squared. Standard deviation uses the same units as the original observations, so it is often easier to discuss alongside the mean. For example, a mean of 20 inches and a standard deviation of 3 inches are expressed on the same scale; variance of 9 square inches is useful for calculations but less direct to interpret.
Neither statistic gives a universal label such as “good,” “bad,” or “normal.” What counts as substantial spread depends on the measurement, collection process, and purpose. A variance from one scale also cannot be compared directly with a variance from another scale because the units are squared.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Paste or type numeric values in the Data field. Separate values with commas, spaces, tabs, line breaks, or semicolons. For example, 2, 4, 6 produces a mean of 4 and a sum of squared deviations of 8. The calculator needs at least two values it can parse before it shows results.
Use one consistent unit and include the observations you intend to analyze. Remove column headings and unit labels. Non-numeric pieces are ignored, so a pasted note or malformed value may leave fewer observations in the calculation than expected.
Compare the displayed count with the number of observations in your source list. Negative numbers and decimal values are valid. If the count is lower than expected, inspect separators and remove text that is not part of a number.
Read sample variance when your list is a sample from a larger group, and population variance when the list contains the complete group of interest. Both appear in the results; the sample variance is emphasized.
Review the mean, sum, count, and sum of squared deviations. The displayed calculation steps show the mean, squared deviations, their sum, and each variance denominator. Results are formatted to at most six decimal places in the main display; very large or very small values may use scientific notation.
The mean is (2 + 4 + 6) / 3 = 4. The deviations from the mean are −2, 0, and 2; after squaring, they are 4, 0, and 4. Their sum is 8. The sample variance is 8 / (3 − 1) = 4 and the population variance is 8 / 3 ≈ 2.666667. The corresponding standard deviations are 2 and approximately 1.632993. This makes the denominator distinction visible while keeping the observations fixed.
Use cases
See how the tool fits into real work and everyday tasks.
A student can enter a short list, follow the displayed deviations, and compare the n − 1 and n denominators. This is useful for checking a worked exercise when the assignment specifies which variance convention to report.
An analyst can summarize readings such as part dimensions or service times, then report a standard deviation in the same unit as the readings. The statistic helps describe spread; it does not decide whether a process meets a target or specification.
When comparing two batches measured in the same units, use a consistent definition and data inclusion rule. Consider the means and the actual observations too, since equal variances can hide different patterns and a single extreme value can shift the result.
Q&A
Find concise answers to common questions and confusing cases.
They divide the same sum of squared deviations by different amounts. Population variance divides by n to describe the full group entered; sample variance divides by n − 1 when the entered observations are used to estimate a larger population’s variance.
The calculator requires at least two parsed observations. With one value, sample variance also has a zero denominator because n − 1 equals zero. Check that separators and any copied text have not caused valid values to be skipped.
Text fragments that cannot be converted to numbers are ignored. Remove headings, units, and notes, and check that values are separated by commas, whitespace, or semicolons. Then compare the result count with the cleaned list.
No: squared deviations and their sum cannot be negative, and the valid denominators are positive for the supported input size. If the display is empty, check whether fewer than two numeric values were parsed.
Notes
Review scope, result limitations, and important precautions before use.
A variance is a descriptive summary of the values entered. It does not assess whether a sample represents a population, whether observations are independent, whether a process is acceptable, or whether a difference is statistically significant. Use the sampling plan and relevant measurement or business criteria for those judgments.
Because deviations are squared, extreme values can have an outsized effect. Check unusual observations against their source records before deciding how to handle them; do not remove a value solely because it makes the variance larger. Keep the unit, group definition, and sample or population convention consistent when reporting or comparing results. The page skips non-numeric input, so confirm the displayed count before relying on an answer.
Related
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