Two investments can have the exact same average annual return and still be nothing alike. One might deliver something close to that average almost every year; the other might swing wildly above and below it, averaging out to the same number only over the long run. Standard deviation is the tool that tells these two apart. It is the most common way to measure investment risk numerically, turning “this feels riskier” into an actual number you can compare across investments.

The standard deviation formula. To find the standard deviation of a set of historical annual returns, work through four steps: find the mean return, find how far each year’s return deviates from that mean, square each deviation, then average the squared deviations and take the square root.

Standard Deviation = √[ Σ(x − mean)² ÷ (n − 1) ]

Here, x stands for each individual return, mean is the average of all the returns, and n is the number of returns in the set. Dividing by n − 1 rather than n is called the sample standard deviation — the standard approach when your data is a limited sample of history, like five years of returns, rather than every return an investment will ever produce.

Worked example. Suppose two hypothetical funds each averaged a 7% annual return over the same five years, but got there very differently. Fund A’s annual returns were: 8%, 12%, −6%, 15%, 6%. Fund B’s annual returns were: 6%, 7%, 8%, 6%, 8%.

Step 1 — find the mean. Both funds add up to 35 across five years, for a mean of 35 ÷ 5 = 7% each.

Step 2 — find each year’s squared deviation from the mean. Fund A: (8−7)²=1, (12−7)²=25, (−6−7)²=169, (15−7)²=64, (6−7)²=1, for a sum of squared deviations of 260. Fund B: (6−7)²=1, (7−7)²=0, (8−7)²=1, (6−7)²=1, (8−7)²=1, for a sum of squared deviations of 4.

Step 3 — divide by n − 1 (5 − 1 = 4) to find the variance. Fund A variance = 260 ÷ 4 = 65. Fund B variance = 4 ÷ 4 = 1.

Step 4 — take the square root to find the standard deviation. Fund A standard deviation = √65 ≈ 8.06%. Fund B standard deviation = √1 = 1%.

Both funds averaged the same 7% return, but Fund A’s standard deviation is about eight times larger than Fund B’s. Fund A’s actual yearly returns ranged from a 6% loss to a 15% gain; Fund B never strayed more than a point from its average. An investor looking only at average return would see two identical funds. Standard deviation reveals they carry very different risk.

What standard deviation tells you. A larger standard deviation means returns are spread out further from the average — the investment has been more volatile, with bigger swings in both directions. A smaller standard deviation means returns cluster tightly around the average — more predictable, but not necessarily “better,” since a low-volatility investment can also mean lower growth potential. Standard deviation says nothing about direction; a fund that mostly went up in big jumps and a fund that mostly went down in big jumps could show the same standard deviation. That is why standard deviation is almost always read alongside average return, not instead of it — together, they describe both what an investment tends to earn and how much uncertainty surrounds that number.

Related reading: standard deviation is the risk measure behind the diversification math in Modern Portfolio Theory, and a close relative of beta in the Capital Asset Pricing Model (CAPM), which measures risk relative to the market instead of in isolation. For a plain-language introduction to investment risk, see Understanding Investment Risk.