Standard deviation calculator
Measure how spread out a list of numbers is around its mean. A small standard deviation means values sit close to the average, and a large one means they are spread out. Students, scientists and analysts use it to describe data.
- Runs in your browser
- Free, no account needed
- Copy or download the result
Result
Example
2, 4, 4, 4, 5, 5, 7, 9
Count: 8 Mean: 5 Variance: 4.57142857143 Standard deviation: 2.1380899353
How to use the standard deviation calculator
- Paste your numbers in the Numbers box, separated by commas, spaces, semicolons or new lines.
- Under Data type, pick Sample (divide by count minus one) or Population (divide by count).
- Press Run to see Count, Mean, Variance and Standard deviation.
- Press Copy result or Download to save the results.
How it works
Variance = the sum of (each value - mean) squared, divided by count minus one for a sample or by count for a population. Standard deviation is the square root of the variance.
Sample mode needs at least two numbers. Population mode works with a single number, which gives 0.
Values are shifted by the first number before squaring, which keeps results accurate when numbers are large and close together.
Uses floating point math and shows results to 12 significant digits. Up to 5,000 numbers are accepted.
Everything runs in your browser. Your input is not uploaded or stored.
Questions and answers
What is the difference between sample and population standard deviation?
Use population when your list includes every member of the group. Use sample when your list is only part of a larger group, since dividing by count minus one corrects for a sample's tendency to understate spread.
How do you calculate standard deviation?
Find the mean, subtract it from each value and square the results, then add those squares. Divide by count for a population or count minus one for a sample, then take the square root.
What is the standard deviation of 2, 4, 4, 4, 5, 5, 7, 9?
The mean is 5. The population standard deviation is exactly 2, and the sample standard deviation is about 2.138.
What is variance?
Variance is the average squared distance from the mean. Standard deviation is its square root, which puts it back in the same units as your data.