Standard Deviation Calculator

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Standard Deviation measures the volatility or dispersion of returns around the average, indicating the level of investment risk. Enter a list of numbers that you want to measure risk or variation for. Example:
• Year-wise returns
• Monthly returns
• Prices
• Any numerical data series More info →

Input

Enter values separated by commas.

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How This Calculator Works

Standard deviation measures how spread out a set of numbers is around their average. For investment returns, a higher standard deviation means the returns jump around more, which means more risk. The calculator gives two versions: one for a complete set of numbers and one for a sample.

The Formulas

Population SD = √ [∑(x − mean)² ÷ n]
Sample SD = √ [∑(x − mean)² ÷ (n − 1)]

x = each value · mean = average of all values · n = number of values

What Each Input Does

Values: The numbers to analyse, separated by commas, for example yearly returns: 10, 12, 8, 15, 9, 11. At least two are needed.

Step by Step

The average (mean) of all values is worked out.
Each value's distance from the mean is squared, and these are added up.
The total is divided by n (population) or n − 1 (sample).
The square root of each gives the standard deviation, shown to 2 decimals.

Reading the Result

Sample – use when your numbers are a sample of a larger set, such as a few years of returns.

Population – use when your numbers are the whole set.

Quick Example

Values 10, 12, 8, 15, 9, 11. The mean is 10.83. The population standard deviation is 2.27 and the sample standard deviation is 2.48.