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Variance Calculator

Calculate population and sample variance from a list of numbers. See the mean, squared deviation table and standard deviation, computed in your browser.

Enter at least one number to compute the population and sample variance.

What is the Variance Calculator?

The ByteTools Variance Calculator measures how spread out a data set is. Paste your numbers and it returns both the population variance (dividing by n) and the sample variance (dividing by n − 1), together with the mean, the sum of squared deviations and the matching standard deviations.

  • Population (÷ n) and sample (÷ n − 1) variance together
  • Mean, count, sum of squared deviations and both standard deviations
  • Full deviation table: value, deviation and squared deviation
  • Accepts commas, spaces, semicolons or new lines as separators
  • Copy-ready summary of every statistic
  • 100% private — your data never leaves your browser

How to use the Variance Calculator

  1. 1

    Paste or type your numbers, separated by commas, spaces or new lines.

  2. 2

    Read the population variance (÷ n) and sample variance (÷ n − 1) side by side.

  3. 3

    Check the mean, count and standard deviations in the summary grid.

  4. 4

    Review the deviation table to see how each value contributes.

  5. 5

    Click Copy to grab the full summary.

About the Variance Calculator

The ByteTools Variance Calculator measures how spread out a data set is. Paste your numbers and it returns both the population variance (dividing by n) and the sample variance (dividing by n − 1), together with the mean, the sum of squared deviations and the matching standard deviations.

Variance is the core building block of statistics: it feeds standard deviation, z-scores, confidence intervals and regression. Students, analysts and researchers use this tool to check homework, verify spreadsheet formulas or get a quick feel for how variable a measurement is. A full deviation table shows each value, its distance from the mean and that distance squared.

Everything is computed 100% locally in your browser with JavaScript using the two-pass mean-then-deviations method. Your data is never uploaded or stored anywhere, so it stays private and the result appears instantly as you type.

Frequently asked questions

How do you calculate variance?

Find the mean, subtract it from each value, square each difference, then average the squared differences. For population variance you divide the sum of squares by n; for sample variance you divide by n − 1. This tool shows every squared deviation so you can follow the whole calculation.

What is the difference between population and sample variance?

Population variance divides by n and describes a complete data set. Sample variance divides by n − 1 (Bessel's correction) because a sample tends to underestimate the true spread. If your numbers are only a sample of a larger group, use the n − 1 version.

What is the relationship between variance and standard deviation?

Standard deviation is simply the square root of variance. Variance is expressed in squared units, which is awkward to interpret, so the standard deviation converts the spread back into the original units of your data. The calculator reports both.

Can variance be negative?

No. Variance is an average of squared deviations, and squares are never negative, so variance is always zero or positive. A variance of exactly zero means every value in the data set is identical.

What does a high variance mean?

A high variance means the values are widely scattered around the mean, while a low variance means they cluster tightly. Whether a number counts as high depends on the scale of your data, which is why comparing standard deviation to the mean is often more intuitive.

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