Beta Calculator

Calculate how much an instrument moved relative to a benchmark, from two series of returns you enter.

Beta is the slope of a line, and this beta calculator fits that line from figures you supply. Plot one holding's return against its benchmark's return for each period, draw the least-squares line through the resulting scatter, and beta is that line's gradient: a beta of 1.28 says that in a period when the benchmark moved one point, this holding moved 1.28 points on average across the record measured. Fitted against a broad index, that gradient is what most people mean by market beta.

Formula: beta = covariance(asset, benchmark) / variance(benchmark)

Your figures

Returns by period

One row per period, oldest first, with both returns as a percentage of the value at the start of that period. Enter losses as negative figures. Any period length works, as long as both columns and every row use the same one.

Asset return 1

Benchmark return 1

Asset return 2

Benchmark return 2

Asset return 3

Benchmark return 3

Asset return 4

Benchmark return 4

Asset return 5

Benchmark return 5

Results

Beta

1.28

points of asset movement for each point of the benchmark, across 5 periods

Correlation with the benchmarkBetween −1 and 1 always, because it divides by both dispersions and the scale cancels. Beta divides by the benchmark's alone, which is why it has no such ceiling.: 0.913
R² — variation the benchmark explainsThe share of the asset's movement the benchmark accounts for. The rest came from somewhere else, and a slope fitted through a low R² is a line drawn through a cloud.: 83.4%
Asset standard deviation per periodThe sample figure, n − 1. How far the asset's own returns spread around their mean.: 3.502%
Benchmark standard deviation per periodThe same measure on the other column. Beta carries the ratio of these two inside it.: 2.501%
Covariance with the benchmarkThe numerator of beta, in squared percentage points, so it reads as nothing on its own. Sample convention, n − 1.: +7.999
Benchmark varianceThe denominator of beta, in the same squared units. The n − 1 divisor is in both and cancels, which is why beta itself is convention-free.: 6.257
Mean asset return per periodThe arithmetic mean of the column entered, not a compound growth rate.: +0.160%
Mean benchmark return per period: +0.720%
Periods countedBlank rows are not counted. Everything above is estimated from this many paired observations, and a short record moves a long way on one more of them.: 5

What this means

Across the 5 periods entered, the asset moved 1.278 points for each point the benchmark moved. That slope is beta: the least-squares line through the scatter of one column against the other, with the covariance of +7.999 over its numerator and the benchmark's variance of 6.257 underneath. It keeps the ratio of the two volatilities — 3.502% a period against 2.501% — inside it, which is why beta has no ceiling however closely or loosely the two are tied together. Correlation asks the other question of the same two sums, dividing by both dispersions so the scale cancels: at 0.913 it says the benchmark accounts for 83.4% of the asset's variation, and whatever moved the rest was not the benchmark. The two figures are worth reading together, because a slope is only as useful as the fit underneath it.

Beta describes movement, not return. A beta above 1 says the asset amplified the benchmark's moves in both directions over the record entered — it does not say the asset earned more, and this series is an example of the two coming apart.
Frequency is part of the statistic. Beta over sixty daily returns and beta over twenty-four monthly returns are two different figures about the same holding, and they routinely disagree.
Every dispersion figure here — the variance, the covariance, the standard deviations and the tracking error — divides by n − 1 rather than by n, because the mean subtracted from each observation was itself estimated from the same handful of returns. Across twelve observations that lifts a variance or a covariance by 12 ÷ 11, about 9.1%, and a standard deviation or a tracking error by the square root of that, about 4.4% — enough either way to move the second decimal place. It is also the convention published performance statistics are quoted on.
Both columns must describe the same periods in the same order. A period filled in on one side and left blank on the other is refused rather than dropped, because shortening one column would pair every later return with the wrong period's benchmark — an error that changes the answer without changing anything visible.
The benchmark is whatever series you entered in the second column. A fund, a sector, a single competitor or your own previous strategy are all valid choices, and beta means the same thing against each of them.
Nothing here is fetched. The returns, the benchmark, the rate and the beta are all as entered, so the same arithmetic works on a backtest, a factsheet and a live account. The risk-free rate a field opens with is a round illustration, not a current market rate.
This describes a record that has already happened. It summarises the figures entered and says nothing about the ones that follow them, and no particular level of it carries a meaning beyond the arithmetic that produced it.

The link reopens this calculator with the same numbers. Nothing you enter is sent to a server.

Continue with these figures

About the Beta calculation

The two columns are yours to type in — the asset's return and the benchmark's return for the same period, oldest first, three periods at minimum and sixty at most. The first column can hold one stock or a whole account, so the same page serves as a stock beta calculator and as a portfolio beta calculator, because the arithmetic does not care which series it is fitting. Nothing is fetched and no index is assumed, because a benchmark is only whatever series you have decided to be measured against: a broad index, a sector, one competitor, a fund, or the strategy you ran last year.

Beside the slope it reports the correlation and R², which ask a different question of the same two columns. The slope says how far the asset moved per point of benchmark; the fit says how much of the asset's movement the benchmark accounts for at all. A beta of 1.3 sitting on an R² of 20% is a line drawn through a cloud, and a hedge sized on it will not behave the way the slope implies.

Beta formula

ā = Σ aᵢ ÷ n                b̄ = Σ bᵢ ÷ n

cov(a, b) = Σ (aᵢ − ā)(bᵢ − b̄) ÷ (n − 1)
var(b)    = Σ (bᵢ − b̄)² ÷ (n − 1)

beta      = cov(a, b) ÷ var(b)
          = Σ (aᵢ − ā)(bᵢ − b̄) ÷ Σ (bᵢ − b̄)²

r         = cov(a, b) ÷ (σₐ × σ_b)
R²        = r²

equivalently:  beta = r × (σₐ ÷ σ_b)

aᵢ, bᵢ: The asset's return and the benchmark's return in period i, both as percentages on the same basis.
ā, b̄: The arithmetic means of the two columns — plain averages of the figures entered, not compound growth rates.
n − 1: The sample divisor. The mean subtracted from each observation was estimated from the same handful of returns, so one degree of freedom has already been spent.
σₐ, σ_b: The sample standard deviations of the two columns, in percentage points per period.
r, R²: Correlation, between −1 and 1, and its square: the share of the asset's variation the benchmark accounts for.

The beta formula — covariance of the two columns over the variance of the benchmark alone — carries the n − 1 divisor in both halves, so it cancels, which is why beta is the same number whichever convention you use. It survives in the covariance and the variance reported underneath, and those are quoted on the sample convention like every other dispersion figure here. Across twelve observations the sample variance and covariance are 12 ÷ 11 — about 9.1% — larger than their population counterparts, which is enough to move a second decimal place. The familiar 4% figure belongs to a standard deviation, which takes the square root and so inherits only √(12 ÷ 11), or 4.4%.

Beta divides by the benchmark's dispersion alone, so the ratio of the two volatilities stays inside it and the result has no ceiling: a small, wild instrument measured against a broad index can slope at 3, and nothing is wrong with the arithmetic when it does. Correlation divides by both dispersions, the scale cancels, and it can never leave ±1. The last line above shows how the two are joined — beta is the correlation multiplied by how much more the asset moves than the benchmark, so a high beta can come from a tight relationship with a volatile asset or from a loose relationship with a very volatile one.

That is why the slope and the fit are reported together rather than separately. Two records can produce the identical beta of 1.28 while one explains 83% of the asset's variation and the other explains 15%. In the first the benchmark is genuinely driving the asset. In the second the slope is a summary of noise, and the standard error around it will be wide enough to include almost any figure you care to name.

One asymmetry catches people out. Least squares treats the benchmark as the input and the asset as the output, so swapping the two columns does not return one divided by beta. In the worked example below the asset-on-benchmark slope is 1.278, while the benchmark-on-asset slope is 0.652 — not 0.782. The second slope is the reciprocal multiplied by R², which is 0.834 here, so the product of the two slopes is always the fit itself and the reciprocal only holds when that fit is perfect.

Beta: a worked example

Five monthly returns for one holding beside the index it is measured against: +4.3% against +2.4%, −2.0% against −1.1%, +3.4% against +3.6%, −1.2% against +1.2%, and −3.7% against −2.5%.

Mean returnsasset (4.3 − 2.0 + 3.4 − 1.2 − 3.7) ÷ 5 = 0.16%; benchmark 3.6 ÷ 5 = 0.72%
Sum of cross-products(4.14 × 1.68) + (−2.16 × −1.82) + (3.24 × 2.88) + (−1.36 × 0.48) + (−3.86 × −3.22) = 31.994
Sum of squared benchmark deviations1.68² + 1.82² + 2.88² + 0.48² + 3.22² = 25.028
Covariance31.994 ÷ 4 = 7.9985
Benchmark variance25.028 ÷ 4 = 6.257
Beta7.9985 ÷ 6.257 = 1.278
Correlation31.994 ÷ √(49.052 × 25.028) = 0.913
R²0.913² = 0.834, or 83.4%

A beta of 1.28 on an R² of 83.4%: the fitted line has the holding moving about a quarter further than the index in each direction, and the index accounts for most of why it moved at all. Note what beta does not say. Over these same five months the asset averaged 0.16% a period against the benchmark's 0.72%, so it moved more and earned less. Beta is a statement about movement, and nothing at all about return.

How to use the Beta calculator

Enter one row per period, oldest first, with both returns as a percentage of the value at the start of that period. Losses go in as negative figures.
Keep both columns on the same frequency and the same basis. Monthly against monthly, total return against total return; a price return in one column and a total return in the other quietly measures the dividend yield as well as the slope.
Clear a row entirely to drop a period. A row with one side filled and the other blank is refused rather than dropped, because shortening one column would pair every later return with the wrong period's benchmark.
Read the R² before the beta. It tells you whether the slope describes a relationship or summarises a scatter, and the two call for very different levels of confidence in the same number.
Carry the beta across to the alpha or Treynor pages, which take it as an input under the same field name rather than assuming one.

Limitations of the Beta calculator

Every calculation makes assumptions. These are the ones that matter here.

A short record produces a slope with an enormous standard error. The five periods in the worked example give a beta of 1.278 with a standard error near 0.33, so the 95% interval runs from roughly 0.23 to 2.33 — the arithmetic is exact and the estimate is not.
Beta measures co-movement, not return and not total risk. It says nothing about the variation the benchmark does not explain, which for a single stock is usually most of it, and a beta of 0.6 on a holding that halved is still 0.6.
Frequency is part of the statistic rather than a detail of it. Beta over sixty daily returns and beta over twenty-four monthly returns are two different figures about the same holding, and for thinly traded instruments the daily figure is biased downwards because prices react a day late.
The estimate assumes the relationship held steady across every period entered. A holding that changed its exposure halfway through the record, or a market that changed regime inside it, has no single slope, and the fitted line averages two behaviours into one that describes neither.
Correlations across risk assets tend to rise sharply in falling markets, and measured betas move with them, which is exactly when a hedge sized from a calm-period figure is being relied upon. The estimate is least stable in the conditions that make it matter most.
No adjustment is applied. There is no shrinkage of the raw slope towards 1, no unlevering for the balance sheet behind it, and no correction for stale prices; the figure reported is the ordinary least-squares slope of the two columns as typed.
A benchmark that returned the same figure in every period is refused, because a flat column has no variation for anything to be measured against and the division would be by zero.

Frequently asked questions about Beta

What does a beta of 1.28 actually mean?

That across the periods entered, the asset moved 1.28 points for each point the benchmark moved, on average, along the best-fitting straight line through the two columns. It is a description of a completed record, not a forecast, and it holds in both directions — the same 1.28 applies to the falls as to the rises.

Why does my beta change when I switch from daily to monthly returns?

Because they are different statistics. Daily returns capture short-horizon co-movement and are affected by when each market closes and how often the instrument trades; monthly returns average that away. Neither is the correct one — the right frequency is the one that matches the horizon you care about, and the two routinely disagree by a wide margin.

How is beta different from correlation?

Correlation measures how tightly the two series move together and is capped at ±1. Beta measures how far one moves per unit of the other and has no cap, because it divides by the benchmark's dispersion alone while correlation divides by both. Beta equals the correlation multiplied by the ratio of the two standard deviations, so a high beta can come from a strong relationship or from a merely volatile asset.

How many periods do I need for a meaningful beta?

Three is the arithmetic minimum and is nowhere near enough. Two points fit a line exactly, so a beta from two would arrive with a correlation of 1 whatever the numbers were, and even five leaves a confidence interval several times wider than most readers assume. Thirty-six or sixty monthly returns are the usual working conventions, and they buy precision at the cost of assuming the relationship held that long.

Can beta be negative?

Yes, and it is reported without any warning colouring. A negative beta means the asset tended to move against the benchmark across the record entered — the ordinary result for a short position, an inverse product, and occasionally for genuinely defensive assets over particular stretches. It is a description of direction, not a loss.

Does a higher beta mean the asset is riskier?

It means the asset amplified the benchmark's moves over the record measured. Whether that is riskier depends on what else is held: inside a diversified portfolio the market-linked part is the part that cannot be diversified away, while for a concentrated account the variation the benchmark does not explain — everything R² leaves out — is often the larger danger and beta says nothing about it.

Why is the beta of the benchmark on the asset not simply one divided by beta?

Because least squares minimises errors in one direction only, treating the column on the horizontal axis as measured exactly. Swap the columns and you minimise a different set of errors, so you get a different line. The product of the two slopes always equals R², which means the reciprocal only holds when the fit is perfect.

Last reviewed 29 August 2026. See our methodology and editorial policy.

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