Standard Deviation Calculator

Find the sample or population standard deviation, variance, mean and standard error of a data set with full working.

Also known as std dev calculator, sd calculator, sample standard deviation.

Enter values

Result

Sample standard deviation s

5.23722937

Variance: 27.42857143
Mean: 18
Count: 8
Standard error of the mean: 1.8516402

Step-by-stepShow

x̄ = 144 ÷ 8 = 18
Σ(x − x̄)² = 192
s = √(192 ÷ 7) = 5.23722937

About the Standard Deviation Calculator

Find the sample or population standard deviation, variance, mean and standard error of a data set with full working.

Also known as: std dev calculator, sd calculator, sample standard deviation, population standard deviation, stdev, σ calculator.

How to use this calculator

Enter data set, data is a.
The result updates instantly as you type — press Calculate (or Enter) at any time.
Open “Step-by-step” to see how the answer was worked out.
Use Copy result or Share to save the answer or send a link with your inputs.

Standard Deviation formula

s = √(Σ(x − x̄)² / (n − 1))

Worked example

Using the values pre-filled in the calculator above:

Data set: 10, 12, 23, 23, 16, 23, 21, 16
Data is a: Sample

the calculator returns:

Sample standard deviation s: 5.23722937
Variance: 27.42857143
Mean: 18
Count: 8

Working

x̄ = 144 ÷ 8 = 18
Σ(x − x̄)² = 192
s = √(192 ÷ 7) = 5.23722937

Frequently asked questions

Sample or population — which should I use?

Use population when your data includes every member of the group you care about. Use sample (dividing by n − 1, Bessel’s correction) when the data is a subset used to estimate a larger population — the most common case.

What does standard deviation tell you?

How spread out values are around the mean. In a normal distribution about 68% of values lie within one standard deviation of the mean and 95% within two.