Why is variance measured in squared units?
Because deviations are squared during calculation, the resulting variance is expressed in squared units of the original measurement (e.g. dollars² or meters²). Taking the square root gives standard deviation in original units.
Why do we square deviations instead of taking absolute values?
Squaring treats deviations algebraically smoothly (differentiable for calculus), penalizes larger outliers more heavily, and allows variances of independent variables to be summed directly.
What is the relationship between variance and standard deviation?
Standard deviation is the positive square root of variance: Standard Deviation = √Variance, and Variance = (Standard Deviation)²
When should I use sample variance versus population variance?
Always use sample variance (dividing by n - 1) unless you have gathered data from every single member of the complete target population.
Can variance be negative?
No. Sums of squared numbers are always greater than or equal to zero, so variance can never be negative.
How accurate is the result?
Results use JavaScript's 64-bit floating point — accurate to 15+ significant digits for most calculations.
Can I enter decimal numbers?
Yes, decimals are fully supported.
Is it free?
Yes, completely free.
Does it show the formula?
Yes, the formula is displayed on the page.
Can I use it on mobile?
Yes, the calculator is fully responsive.
Does it save my inputs?
No data is stored — all calculations are done locally in your browser.
What if I get an error?
Check for invalid inputs such as division by zero or negative square roots.