Standard Deviation Calculator
Find the standard deviation and variance of any data set. Paste or type your numbers and the calculator shows the mean, count, sum, and both the sample and population results side by side.
How to calculate standard deviation
- Enter your numbers, separated by commas, spaces, or new lines.
- Decide whether your data is a full population or a sample from one.
- Read the matching standard deviation and variance from the results.
Examples
Population standard deviation
2, 4, 4, 4, 5, 5, 7, 9
Mean = 5, population SD = 2, population variance = 4
Sample variance
2, 4, 6
Mean = 4, sample variance = 4, sample SD = 2
Frequently asked questions
What does standard deviation tell you?
Standard deviation measures how spread out your numbers are around the mean. A small value means the data points sit close to the average, while a large value means they are more scattered. It is reported in the same units as your data.
What is the difference between sample and population standard deviation?
Population standard deviation divides the squared differences by N, the count of values, and is used when your numbers cover the entire group. Sample standard deviation divides by N minus 1, which corrects for the bias you get when estimating a larger population from a smaller sample.
Should I use the sample or population version?
Use the population version only when your data includes every member of the group you care about. In most real analysis you have a sample drawn from a bigger population, so the sample standard deviation, dividing by N minus 1, is the right choice.
What is variance and how does it relate to standard deviation?
Variance is the average of the squared differences from the mean. Standard deviation is simply the square root of the variance, which converts the spread back into the original units so it is easier to interpret.
Why do I need at least two values for the sample result?
Sample variance and standard deviation divide by N minus 1. With a single value that divisor is zero, so the result is undefined. The calculator returns the sample figures only once you enter two or more numbers.
Is my data sent anywhere?
No. The calculation runs entirely in your browser, so your numbers never leave your device.
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