Stock Beta Calculator

The Stock Beta Calculator measures how a stock tends to move relative to a market benchmark such as the S&P 500, FTSE 100, or Nikkei 225. Beta is a core input to the Capital Asset Pricing Model (CAPM), to expected-return calculations, to risk-adjusted performance ratios, and to portfolio construction. This tool accepts three input modes — periodic returns, raw price series, or summary statistics — and reports beta, alpha, Pearson correlation, R², CAPM expected return, and a side-by-side scatter with the regression line.

How to Use

1. Pick periodic returns if you already have % returns, prices if you only have closing prices, or summary statistics if you only know the standard deviations and correlation.
2. Paste paired observations for the stock and the benchmark. Values can be separated by commas, spaces, or newlines.
3. Set the risk-free rate and the expected market return to compute the CAPM expected return for the stock.
4. Use n - 1 (sample) for forecasting future risk, or n (population) when you have the full historical universe.
5. Review the beta value, classification, alpha, R-squared, scatter plot with regression line, CAPM expected return, and the step-by-step breakdown.

Beta Formula

Reading the Beta Number

• β > 1 — the stock amplifies index moves. Useful when you want exposure to market beta during expansion phases, but it cuts both ways in drawdowns.
• β ≈ 1 — the stock tracks the index closely. Many large-cap equities and broad index funds sit here.
• β < 1 — defensive. Utilities, consumer staples, and many dividend stocks have historically printed betas below 1.
• β < 0 — inverse. Inverse ETFs and some hedges fall here. A negative beta is rare for a long-only single stock.

What Makes This Beta Calculator Different

• Three input modes — paste returns, raw prices, or summary statistics. Most calculators only accept returns.
• Full regression output — beta, alpha, correlation, R², systematic vs unsystematic risk decomposition.
• CAPM expected return — automatic plug-in of beta into the cost-of-equity formula with editable risk-free rate and market return.
• Sector benchmark lane — visual comparison of your computed β against typical sector betas (utilities, staples, healthcare, industrials, technology, small-cap growth).
• Sample vs population denominator — explicit toggle so you can match academic, CFA, or industry conventions.
• Step-by-step breakdown — every term in the covariance / variance computation is shown so you can verify by hand or in a spreadsheet.

Sample vs Population Variance

Use the sample denominator n - 1 when your data is a sample drawn to estimate forward-looking risk. Use the population denominator n only when the data covers the full universe you care about. Beta is the same when the same denominator is used for both the covariance and the variance, but the convention you report matters when comparing across data providers.

Tips for Reliable Beta Estimates

• Use at least 30 paired observations. CFA convention is 60 monthly observations (5 years).
• Use the same return frequency for both series (daily with daily, weekly with weekly).
• Align dates exactly — a one-day mismatch can swing beta meaningfully for volatile stocks.
• Watch for thin trading — illiquid stocks can show artificially low beta because of stale prints.
• Outliers (earnings, splits, dividends) can drag beta. Consider winsorizing or using log returns for robustness.

FAQ

What does a stock beta calculator do?

It measures how the price of a stock tends to move relative to a market benchmark. A beta of 1 moves with the index, beta above 1 amplifies index moves, beta below 1 dampens them, and a negative beta moves in the opposite direction.

What is the formula for beta?

Beta equals the covariance between the stock return and the market return divided by the variance of the market return. Equivalently, beta equals the correlation between the two series multiplied by the ratio of the stock standard deviation to the market standard deviation.

What does a beta of 1.5 mean?

A beta of 1.5 implies that, on average, when the market moves 1% the stock moves about 1.5% in the same direction. It is more volatile than the benchmark and carries more systematic risk.

Should I use sample or population variance?

Use the sample denominator n - 1 when your observations are a sample drawn to estimate forward-looking risk. Use the population denominator n only when the data covers the full universe you care about. Both produce the same beta when the same denominator is used for the covariance and variance, but the convention matters when reporting.

How does R-squared relate to beta?

R-squared is the square of the correlation between stock and market returns. It tells you how much of the stock variance is explained by market moves; the rest is unsystematic, stock-specific risk that diversification can reduce.

What is alpha in the regression?

Alpha is the intercept of the regression of stock returns on market returns. It estimates the average return left over after the market component is removed. Persistently positive alpha is associated with skill or mispricing and is what active managers try to deliver.

Can I use weekly or monthly returns?

Yes. Beta is unitless and works for any return frequency, but both series must use the same frequency and be aligned by date. Daily, weekly, and monthly windows commonly produce different beta estimates because of noise and serial correlation.