Standard Deviation Calculator
Calculate standard deviation, variance, and mean from a data set. Population and sample. Free calculator.
What Standard Deviation Tells You
Standard deviation measures how spread out data is from the average. Low SD: Data points cluster near the mean (consistent). High SD: Data is widely spread (variable). In a normal distribution: 68% of data falls within 1 SD of the mean, 95% within 2 SD, and 99.7% within 3 SD. This is why outliers (beyond 3 SD) are so rare and noteworthy.
Sample vs Population Standard Deviation
Population SD (sigma): Used when you have data for the entire population. Divide by N. Sample SD (s): Used when your data is a sample from a larger population. Divide by N-1 (Bessel correction). In practice, you almost always use sample SD because you rarely have complete population data. The difference shrinks as sample size grows.
In investing, standard deviation IS risk. The S&P 500 has a historical SD of 15-16%, meaning a 30% swing in either direction is a once-per-generation event — but it does happen.
