Example 1
- 2
- 8
3
What is the deviation of 2 and 8? 3. Two numbers, divide by 2.
Standard deviation calculator
Enter two numbers, or a list in the first field. The calculator computes the population standard deviation: mean, variance over n, then the square root. 2 and 8 give 3. The list 2, 4, 4, 4, 5, 5, 7, 9 gives 2.
This is a population deviation: the divisor is n, not n−1. Two numbers in separate fields still work. A list in the first field, separated by commas or spaces, uses n entries.
Results
Enter data and click Calculate.
How it works
Standard deviation of two numbers is the square root of the population variance. The calculator uses the mean m = (a+b)/2, then ((a−m)²+(b−m)²)/2 and the root. 2 and 8 have mean 5 and give 3. The result goes into the field raw, not through a fixed place count.
This is a population of n=2, not a sample. School sample variance divides by n−1; here the denominator is 2. 1 and 1 have mean 1 and variance 0, so the deviation is 0. Two equal numbers do not spread.
The fields are number 1 and number 2, both with min=0. An empty field is read as 0. 0 and 10 give 5, because the mean is 5, the squared deviations sum to 50, over 2 that is 25, and the root is 5.
The three-number neighbour divides the variance by 3, not by 2. Variance of n numbers takes a list and leaves σ², with no root. Here you always type two values and get σ.
The header units switch does not multiply anything. 2 and 8 stay 3 whatever the label says. The engine is calculator-odchylenie-standardowe.js, not the generic branch with six decimals.
2 and 8 give 3. 1 and 1 give 0. 0 and 10 give 5. That is the whole card: two numbers, divide by 2.
Formula
σ = √(Σ(x − m)² / n), m = mean of n numbers
How to use
- Type two numbers, for example 2 and 8.
- Click Calculate. The deviation comes out 3.
- 1 and 1 give 0. 0 and 10 give 5.
- An empty field counts as 0. The divisor is 2, not n−1.
- Three numbers live on the neighbouring card. There the denominator is 3.
2 and 8 give 3
Deviation of two numbers, population n=2. 2 and 8 give 3. 1 and 1 give 0. Divides by 2, not by n−1.
- deviation
- The square root of the variance. 2 and 8 give 3. 0 and 10 give 5.
- population
- The denominator is n, here 2. This is not a sample with n−1.
- variance
- Sum of squared gaps from the mean, over 2. Then the root. 1 and 1 give variance 0.
Examples
Example 2
- 1
- 1
0
What is the deviation of 1 and 1? 0. Same numbers, zero spread.
Example 3
- 2, 4, 4, 4, 5, 5, 7, 9
2
What is the deviation of 2, 4, 4, 4, 5, 5, 7, 9? 2. Eight numbers, mean 5, variance 4.
Related calculators
Common questions
What is the deviation of 2 and 8?
3. Mean 5, variance 9, root 3. Raw display, no six zeros.
Does the calculator divide by n−1?
No. It divides by n. Two numbers use n = 2. A longer list uses that length. This is a population deviation, not a sample.
What do 1 and 1 give?
0. Mean 1, both deviations zero.
What does the list 2, 4, 4, 4, 5, 5, 7, 9 give?
2. Mean 5, variance 4, square root 2.
What if I leave a field empty?
The engine reads empty as 0. Not a list and not an error, only zero in this code.
How is this different from the three-number card?
Here two fields and divide by 2. There three fields and divide by 3.
Where is variance alone?
On the variance of n numbers card. Here you get the square root at once.
Can the result be a fraction?
Yes, when the root is not an integer. Then you see the full JS string, not six decimal places.
Does min=0 block a minus?
The fields have min=0. Negatives are not the point of this form.
Does the order of a and b change the result?
No. 2 and 8 and 8 and 2 both give 3.
Knowledge sources
The calculator divides by n, not n−1. This is the population figure from the numbers you type.
Page updated in 2026.