Stock Beta Coefficient Calculator
Beta measures a stock's sensitivity to overall market moves and is a core input to the capital asset pricing model. Enter the stock's period returns and the market's period returns as two equal-length lists. The calculator computes the covariance between them and the variance of the market, then divides to give beta, along with the correlation for context. Beta is based on historical data and is an estimate, not a forecast.
Beta formula
Covariance = mean of (stock - mean stock)(market - mean market)
Market variance = mean of (market - mean market)^2
Beta = covariance / market variance
Correlation = covariance / (stdev stock * stdev market)
Both series must have the same number of values. Population definitions (dividing by n) are used; this does not affect beta because the divisor cancels in the ratio.
Worked example
Stock 3, -2, 5, 1, 4; market 2, -1, 3, 1, 3 (n = 5):
- Mean stock = 2.20; mean market = 1.60.
- Covariance = 3.68; market variance = 2.24.
- Beta = 3.68 / 2.24 = 1.64.
Beta coefficient: frequently asked questions
What is a stock's beta?
Beta measures how much a stock's returns move relative to the overall market. A beta of 1 means the stock tends to move with the market. Above 1 means more volatile than the market; below 1 means less volatile; a negative beta means it tends to move opposite the market. Beta equals the covariance of the stock and market returns divided by the variance of the market returns.
How do I enter the data?
Enter the stock's returns and the market's returns as two comma-separated lists with the same number of values, each pair representing the same period. The calculator computes the covariance between the two series and the variance of the market series, then divides them.
Should I use sample or population statistics?
Beta is a ratio of covariance to variance, and the same divisor (whether n or n-1) appears in both, so it cancels. This calculator uses population definitions (dividing by n) for both, which gives the same beta as using sample definitions consistently.
What does a beta of 1.3 mean for an investor?
It suggests that, historically, when the market moved 1 percent the stock tended to move about 1.3 percent in the same direction. Higher beta implies greater market-related (systematic) risk and, in theory, a higher expected return to compensate. Beta is historical and does not guarantee future behaviour.
Official sources
- U.S. Securities and Exchange Commission, Investor.gov: Beta.
- U.S. Securities and Exchange Commission, Investor.gov: Stocks.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.