Variance Calculator

A variance calculator is a free tool that computes both population variance and sample variance of any dataset instantly. Type or paste numbers separated by commas, spaces, or new lines — or upload a CSV or TXT file — and the calculator automatically detects your separators, parses the values, and returns variance, standard deviation, and a full descriptive statistics summary.

Beyond variance itself, this calculator also returns mean, sum, count, minimum, maximum, range, and population/sample standard deviation — plus a complete step-by-step breakdown showing every deviation and squared deviation used in the calculation, making it as useful for learning statistics as it is for real analysis.

This tool is built for students, teachers, data analysts, researchers, engineers, scientists, business analysts, financial analysts, and quality assurance professionals. We do not collect or store what you enter.

Paste or type your numbers into the textarea in any format — comma-separated, space-separated, one per line, or a mix of all three. The calculator normalizes your input, discards anything that isn't a valid number, computes the mean, then calculates the deviation and squared deviation of every value from the mean in a single pass before summing them to produce variance.

• →Automatic Separator Detection: Commas, spaces, new lines, tabs, and mixed combinations are all normalized automatically — no manual configuration needed.
• →Population vs. Sample Mode: Choose Population Variance, Sample Variance, or Both to control which formula is calculated and displayed.
• →Step-by-Step Breakdown: Every value's deviation and squared deviation from the mean is shown in a scrollable table for full transparency.
• →File Upload & Drag-and-Drop: Upload a .csv or .txt file, or drag one directly onto the input box, to instantly load a dataset without manual copy-pasting.

Population variance (σ²) is used when your dataset includes every member of the group you care about — for example, the test scores of every student in a single class. It divides the sum of squared deviations by n, the total count.

Sample variance (s²) is used when your dataset is a subset drawn from a larger population — for example, a survey of 200 customers out of a million. It divides by n − 1 instead of n, a correction known as Bessel's correction, which compensates for the tendency of a sample to underestimate the true population variance.

Common mistake: using population variance on sample data systematically underestimates variability. When in doubt about which to use, sample variance is the safer default for any dataset that doesn't represent the entire population of interest — which is why this calculator computes both by default.