Variance calculator

Type a list of numbers, comma, space or semicolon. The calculator computes population variance: sum of squared gaps from the mean, over n. 1, 2, 3, 4, 5 give 2. 2, 2, 2 give 0. 1, 3 give 1.

One text field. It divides by n, not by n−1. Fewer than two numbers leave a blank. An integer variance is a string, a fraction is six decimal places.

Input data

Results

Enter data and click Calculate.

How it works

Variance of n numbers is the mean squared gap from the mean. The calculator builds a list from one field, computes x̄, then Σ(xᵢ − x̄)²/n. 1, 2, 3, 4, 5 have mean 3 and give 2. This is a population, not a sample.

The denominator is n, not n−1. School sample variance subtracts one. Here 1 and 3 give 1, because the mean is 2 and two squared ones over 2. If you divided by n−1 you would get 2.

There is one field: the list. Comma, space and semicolon split the entries. 2, 2, 2 give 0. One number is not enough. The engine then leaves a blank, not a zero.

Deviation of two numbers takes the root after dividing by 2. Deviation of three numbers divides by 3 and also takes the root. Here you stay with variance from any n ≥ 2.

The header units switch does not multiply anything. 1, 2, 3, 4, 5 stay 2 whatever the label says. An integer result is String, a fraction has six decimals.

1, 2, 3, 4, 5 give 2. 2, 2, 2 give 0. 1, 3 give 1. One number leaves the field blank.

Formula

σ² = Σ(xᵢ − x̄)² / n, when n ≥ 2; otherwise blank

How to use

  1. Type a list, for example 1, 2, 3, 4, 5.
  2. Click Calculate. The variance comes out 2.
  3. 2, 2, 2 give 0. 1, 3 give 1.
  4. One number leaves a blank. The divisor is n, not n−1.
  5. The root of two or three numbers lives on the deviation cards.

1, 2, 3, 4, 5 give 2

Population variance from a list. 1, 2, 3, 4, 5 give 2. Divides by n. One number leaves a blank.

variance
Mean squared gap. 1, 2, 3, 4, 5 give 2. 1 and 3 give 1.
population
The denominator is n, not n−1. Two numbers 1 and 3 give 1.
list
One field. Comma, space or semicolon. Below two numbers the result is blank.

Examples

Example 1

  • 1, 2, 3, 4, 5

2

What is the variance of 1, 2, 3, 4, 5? 2. Divides by n=5.

Example 2

  • 2, 2, 2

0

What is the variance of 2, 2, 2? 0. Equal entries, zero spread.

Example 3

  • 1, 3

1

What is the variance of 1 and 3? 1. Over n, not over n−1.

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Standard deviation (3 numbers)

Standard deviation (3 numbers): three numbers.

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Common questions

What is the variance of 1, 2, 3, 4, 5?

2. Mean 3, sum of squares 10, over n=5.

Does the calculator divide by n−1?

No. It divides by n. 1 and 3 give 1, not 2.

What do 2, 2 and 2 give?

0. Mean 2, all gaps zero.

What do 1 and 3 give?

1. Mean 2, two squared ones over 2.

What if I type one number?

The result stays blank. You need at least two values.

How do I separate the numbers?

Comma, space or semicolon. 1, 2, 3 and 1 2 3 are the same list.

How is this different from deviation?

Here you keep σ². The deviation cards take the root and have a fixed field count.

Does a fraction get six decimals?

Yes, when the variance is not an integer. 2 stays the string 2.

Do empty pieces in the list break the result?

Empty chunks after the split drop out. Only numbers remain.

Does list order change the result?

No. 5, 4, 3, 2, 1 also give 2.

Knowledge sources

The calculator divides by n, not n−1. This is the population figure from the numbers you type.

Page updated in 2026.