Standard Deviation Calculator
Compute sample and population standard deviation, variance and mean from your data set instantly.
Calculate standard deviation instantly
The Standard Deviation Calculator computes both the sample and population standard deviation of your data, along with the variance, mean, and count. Paste your numbers and every result appears at once. It saves you from error-prone manual formulas and gives you the exact figures statisticians and students need.
What is standard deviation?
Standard deviation measures how spread out a set of numbers is around their mean. A small standard deviation means the values cluster tightly near the average; a large one means they are spread far apart. It is one of the most important statistics because it quantifies variability — two datasets can share the same mean yet behave very differently, and standard deviation captures that difference.
Sample vs population
There are two versions, and choosing the right one matters. Use population standard deviation (divide by n) when your data includes every member of the group you care about. Use sample standard deviation (divide by n−1) when your data is a sample drawn from a larger population — the n−1 correction, called Bessel's correction, makes the estimate unbiased. Most real-world analysis uses the sample version.
How it is calculated
- Find the mean of all values.
- Subtract the mean from each value and square the result.
- Sum those squared differences.
- Divide by n (population) or n−1 (sample) to get the variance.
- Take the square root of the variance — that is the standard deviation.
How to use it
| Step | Action |
|---|---|
| 1 | Paste at least two numbers, separated by commas, spaces, or new lines. |
| 2 | Read the sample and population standard deviation. |
| 3 | Use the variance and mean shown for deeper analysis. |
Where standard deviation is used
It underpins quality control, finance (where it measures volatility and risk), scientific research, grading curves, and any field that deals with measurement and uncertainty. Understanding the spread of your data is often as important as knowing its average.
Private and free
All calculations run in your browser, with nothing uploaded and no limits. Analyze as much data as you like, free.
Frequently asked questions
What is the difference between sample and population standard deviation?
Population divides by n and is used when you have all the data; sample divides by n−1 and is used when your data is a sample of a larger group.
Which one should I use?
Most analyses use the sample standard deviation, because data is usually a sample. Use population only when you have the entire group.
What is variance?
Variance is the average of the squared differences from the mean. Standard deviation is its square root, in the original units.
How many numbers do I need?
At least two values are required to compute a standard deviation.