Example 1
- 1
- 2
- 3
0.816497
What is the deviation of 1, 2 and 3? 0.816497. Divides by 3.
Standard deviation (3 numbers)
Type three numbers. The calculator computes variance over 3, then the square root. 1, 2, 3 give 0.816497. 2, 2, 2 give 0. 0, 6, 12 give 4.898979.
It divides by 3, not by 2 and not by n−1. A fraction shows six decimals. The two-number neighbour divides by 2.
Results
Enter data and click Calculate.
How it works
Standard deviation of three numbers is the square root of the variance. Mean m = (a+b+c)/3, then the sum of squared gaps from m divided by 3, then the root. 1, 2, 3 have mean 2 and give 0.816497, because √(2/3) is not an integer.
The denominator is 3, not 2. The two-number neighbour divides by 2 and for 2 and 8 shows a raw 3. Here three fields and another divisor, so the same idea with another count of entries gives another σ.
The fields are a, b and c. 2, 2, 2 give 0, because nothing stands off the mean. 0, 6, 12 give 4.898979. An integer result goes as a plain string, a fraction as six decimal places.
Variance of n numbers leaves σ² from a list. Here you always type three values and get the deviation. This is still a population: divide by 3, not by 2.
The header units switch does not multiply anything. 1, 2, 3 stay 0.816497 whatever the label says. The engine is generic, not raw like the two-number card.
1, 2, 3 give 0.816497. 2, 2, 2 give 0. 0, 6, 12 give 4.898979. Three numbers, divide by 3.
Formula
σ = √(((a−m)²+(b−m)²+(c−m)²)/3), m = (a+b+c)/3
How to use
- Type three numbers, for example 1, 2 and 3.
- Click Calculate. The deviation comes out 0.816497.
- 2, 2, 2 give 0. 0, 6, 12 give 4.898979.
- The divisor is 3, not 2 and not n−1.
- Two numbers live on the neighbouring card. There the denominator is 2.
1, 2, 3 give 0.816497
Deviation of three numbers. Variance over 3, then the root. 1, 2, 3 give 0.816497. 2, 2, 2 give 0.
- deviation
- The square root of the variance of three numbers. 1, 2, 3 give 0.816497.
- variance
- Sum of squared gaps from the mean, over 3. Then the root. Not over 2.
- three
- Exactly three fields. The two-number neighbour divides by 2.
Examples
Example 2
- 2
- 2
- 2
0
What is the deviation of 2, 2 and 2? 0. Three equals, zero spread.
Example 3
- 0
- 6
- 12
4.898979
What is the deviation of 0, 6 and 12? 4.898979. Square root of 24.
Related calculators
Common questions
What is the deviation of 1, 2 and 3?
0.816497. Mean 2, variance 2/3, root in six decimals.
Does the calculator divide by 2?
No. It divides by 3. The two-number neighbour divides by 2.
Does it divide by n−1?
No. The denominator is 3. This is a population of three values.
What do 2, 2 and 2 give?
0. Mean 2, all deviations zero. Integer result, no six zeros.
What do 0, 6 and 12 give?
4.898979. Mean 6, variance 24, square root of 24.
Why not the raw root?
A fraction goes through six decimal places. The two-number card shows the raw result.
Where do I compute two numbers?
On the two-number standard deviation card. There the divisor is 2.
Where is variance from a list?
On the variance of n numbers card. Here always three fields and the root.
Does the order of a, b, c change the result?
No. 1, 2, 3 and 3, 2, 1 both give 0.816497.
Does a comma in 1.5 work?
Yes. 1.5 and 1,5 are the same number.
Knowledge sources
The calculator divides by n, not n−1. This is the population figure from the numbers you type.
Page updated in 2026.