Standard Deviation Calculator

Measure how spread out your data is — sample or population, with the working shown step by step.

How to Use This Calculator

Enter your dataset and get both sample and population standard deviation. The rule of thumb: in a normal distribution, about 68% of values fall within 1 SD of the mean, 95% within 2 SD.

Frequently Asked Questions

What is standard deviation in simple terms?

It's the typical distance between any value and the mean. Small SD = data clustered together; large SD = data spread out.

Sample vs population — which do I use?

Use sample SD (÷ n−1) when your data is a subset of a larger group. Use population SD (÷ n) when you have every possible value.

Why divide by n−1 for samples?

Bessel's correction: it makes the estimate unbiased — the sample SD would otherwise be slightly too small.

What does a low SD tell me?

Consistency. In quality control or investing, low variance means outcomes are predictable and close to average.

Practical Example

For the dataset 5, 7, 8, 12, 13, 15, 18, 22:

Mean = 100 ÷ 8 = 12.5
Sample SD ≈ 5.68 → most values sit within about 5.7 of the mean
Population SD ≈ 5.32 (slightly smaller, dividing by n instead of n−1)
In a normal distribution, ≈68% of values fall within one SD of the mean.

What Your Results Mean

Sample SD — spread estimate from a subset (divides by n−1).
Population SD — exact spread when you hold all values (divides by n).
Variance — the squared standard deviation; SD is more intuitive because it's in the same units as the data.