Standard Deviation Calculator
Free standard deviation calculator — sample and population standard deviation, variance, and mean from any list of numbers, with a histogram.
Everyday Uses
Stats homework
Get sample and population standard deviation, variance, and the mean with one paste.
Lab & research
Report the spread of repeated measurements and quantify experimental error.
Finance & risk
Measure the volatility of returns — a higher standard deviation means more risk.
Quality control
Track how tightly a process holds to its target from a sample of outputs.
Frequently Asked Questions
How do you calculate standard deviation?
First find the mean of your numbers. Then subtract the mean from each value, square the result, and add them up (the sum of squares). For a sample, divide by n−1 and take the square root; for a population, divide by n. For 4, 8, 15, 16, 23, 42 the mean is 18, the sample standard deviation is about 13.3, and the population standard deviation is about 12.1.
What is the difference between sample and population standard deviation?
Sample standard deviation divides the sum of squares by n−1 and is used when your data is a sample drawn from a larger group — this is the most common case, and dividing by n−1 corrects for the tendency of a sample to underestimate spread. Population standard deviation divides by n and is used only when your data covers every member of the group.
What does standard deviation tell you?
Standard deviation measures how spread out numbers are around the mean. A small standard deviation means the values cluster tightly around the average; a large one means they are widely scattered. In a normal distribution, about 68% of values fall within one standard deviation of the mean and 95% within two.