Variance Calculator

Find the variance, standard deviation and mean of data.

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Variance

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Standard deviation—

Mean—

How it works

Variance quantifies how much a set of numbers spreads out from its average, and this calculator returns the variance, the standard deviation, and the mean from a list of values. You enter the numbers and choose whether they represent a sample or a whole population, since the two use slightly different formulas. Variance is computed by finding the mean, measuring how far each value sits from it, squaring those distances so positive and negative deviations do not cancel, and averaging the squares. A small variance means the data cluster tightly around the mean, while a large variance means they are widely scattered. The key distinction is the divisor: sample variance divides by one less than the count, known as Bessel's correction, because a sample tends to underestimate the spread of the population it came from, whereas population variance divides by the full count. The standard deviation, the square root of variance, is often more intuitive because it is in the same units as the data. Statisticians, scientists, analysts, and students use variance to measure risk, consistency, and reliability. Enter your values and select the data type to compute all three measures.

Formula

s² = Σ(x − x̄)² / (n − 1); σ² = Σ(x − x̄)² / n

Variance measures how spread out a data set is around its mean. You subtract the mean from each value, square the differences, and sum them. Sample variance divides that sum of squares by the number of values minus one, which corrects for estimating the mean from the sample, while population variance divides by the full count. The standard deviation is simply the square root of the variance.

Source:Descriptive statistics

We review all our tools from time to time to ensure accuracy.

Worked example

Values:1, 2, 3, 4, 5Data set is:sample

Mean = 3; squared deviations sum to 10; sample variance = 10 / 4 = 2.5.

How to use this calculator

1
Enter your values
Enter values and data set is.
2
Adjust the options
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3
Read your result
Variance updates instantly as you type — no button to press.

Frequently asked questions

What is variance?

Variance is a measure of how spread out a set of numbers is around their mean. It is the average of the squared differences between each value and the mean. A larger variance indicates the data are more dispersed, while a variance near zero means the values are all close to the average. It underlies standard deviation and many statistical methods.

What is the difference between sample and population variance?

Population variance divides the sum of squared deviations by the total number of values, used when you have data for an entire group. Sample variance divides by one less than the count, a correction called Bessel's rule, used when your data are a sample meant to estimate a larger population. The sample version is slightly larger to compensate for underestimation.

How does variance relate to standard deviation?

Standard deviation is the square root of variance. Both measure spread, but standard deviation is expressed in the same units as the original data, which makes it easier to interpret, while variance is in squared units. This calculator reports both, so you can use whichever is more convenient for your analysis or assignment.

Why are the deviations squared?

Deviations are squared so that values above and below the mean do not cancel each other out, since squaring makes every difference positive. Squaring also gives more weight to values far from the mean, emphasising large deviations. Taking the square root at the end, to get standard deviation, returns the measure to the original units.

When should I use variance?

Variance is used whenever you need to quantify variability or risk. In finance it measures the volatility of returns, in manufacturing it gauges consistency of a process, in science it describes measurement scatter, and in statistics it is the foundation for tests like ANOVA. A higher variance signals less predictability, which matters across many fields.