Instantly calculate the standard deviation and variance of a list of numbers — sample and population.
Enter the numbers
List of numbers
Separate numbers with spaces, commas or new lines. The standard deviation measures the spread around the mean.
Standard mathematical formulas. Instant in-browser calculation, no account. Exact results for the values you enter.
The standard deviation measures how spread out the values are around the mean. It is the square root of the variance (the average of squared differences from the mean):
For 12, 7, 19, 3, 9, 14: the mean ≈ 10.67, and the sample standard deviation ≈ 5.68. A large deviation means dispersed values.
A measure of how spread out the data is around the mean. The larger it is, the more dispersed the values; a small one means values close to the mean.
Compute the mean, then the average of the squared differences from the mean (the variance), and take the square root. The result is the standard deviation.
The sample deviation divides by (n − 1) and is used when the data is a subset; the population deviation divides by n, when you have all the data.
The average of the squared differences from the mean. The standard deviation is the square root of the variance, in the same units as the data.
A large deviation indicates very varied data (more risk/uncertainty); a small one indicates consistent data, close to the mean.
For many distributions, about 68% of values lie within one standard deviation of the mean, and about 95% within two.
Statistics, quality control, finance (investment volatility), grades and research, to measure the consistency of data.
The mean shows the “center” of the data, while the standard deviation shows how far the values deviate from that center.