Variance Calculator
Calculate both the population and sample variance of a list of numbers, along with the mean. The population variance divides the sum of squared deviations by n, while the sample variance divides by n minus 1.
What this calculator does
The Variance Calculator estimates your result instantly from the values you enter, using standard statistics formulas. Calculate both the population and sample variance of a list of numbers, along with the mean. The population variance divides the sum of squared deviations by n, while the sample variance divides by n minus 1. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.
Result
About Variance Calculator
Enter a comma-separated list of numbers and this calculator returns the mean and two variances. It first finds the mean, then the sum of squared deviations from it. The population variance divides that sum by n, while the sample variance divides by n − 1 (Bessel's correction).
All three figures are shown to four decimals. The sample variance is only defined when you enter more than one value.
Formula & Mathematical Calculation
Population Variance = f(Values (comma-separated))
Calculated according to standard stats formulas implemented in the calculator core.
Calculation Example
Enter the values 4, 8, 15, 16, 23:
- Mean = 66 / 5 = 13.2
- Sum of squared deviations = 84.64 + 27.04 + 3.24 + 7.84 + 96.04 = 218.8
- Population variance = 218.8 / 5 = 43.76
- Sample variance = 218.8 / 4 = 54.7
The panel shows Population Variance 43.76, Sample Variance 54.7, and Mean 13.2.
Key Benefits
- Reports population variance (divided by n) and sample variance (divided by n-1) side by side, so you can pick the right one
- Shows the mean too, which is the basis for both variance figures
- Computes from the sum of squared deviations exactly, to four decimals
- Displays a dash for the sample variance when only one value is entered, since it is undefined there; free and in-browser
How to Use this Calculator
-
Enter your values
Type your numbers into the Values field, separated by commas, for example 4, 8, 15, 16, 23. -
Calculate
Press Calculate to compute the statistics. -
Read the results
Check the Population Variance, Sample Variance, and Mean boxes for the results.
Assumptions & Limitations
What the calculation assumes
- Every value you enter is treated as an exact, known amount.
- Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
- Results use standard published formulas and account only for the values entered above.
- Rounding is applied for display; the underlying calculation uses your full precision.
- Results are returned in the same units you enter, unless the tool states the output unit.
What it does not cover
- Variance Calculator produces a calculated result for reference and learning, not a certified or official measurement.
- Real-world outcomes differ when tolerances, rounding rules or local standards apply.
- Definitions and standards vary by region and change over time; verify the convention that applies to your case.
- Figures are only as accurate as the inputs you supply — check them before acting on the result.
- For work where the result carries real consequences, confirm it against an authoritative source.
Frequently Asked Questions
Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.