Correlation Calculator

Use this correlation calculator to turn a covariance and two standard deviations into the correlation coefficient. See how strongly two assets move together.

What it does

The Correlation Calculator turns a covariance and two standard deviations into the correlation coefficient, a single number between -1 and +1 that measures how two assets move together.

Data sources & parameters

This calculator uses standard financial formulas and runs entirely in your browser. It needs no external rate data — your result is computed only from the values you enter above.

We always strive to use the latest data for every variable so our results and reports are as accurate as possible. Even so, errors are possible — you should not rely on this tool or its report alone, and we accept no liability for any decision made based on it.

The formula

correlation = covariance ÷ (std_dev1 × std_dev2)

How it works

It divides the covariance by the product of the two standard deviations. This rescaling removes the individual volatilities and leaves only the strength and direction of the relationship.

Where it is used

Judging how much diversification a second asset really adds
Standardising a covariance into a comparable -1 to +1 figure
Checking whether two holdings move together, apart, or independently

Worked example

With a covariance of 0.01 and standard deviations of 0.15 and 0.1, the product of the standard deviations is … and the correlation coefficient is …, a strong positive relationship.

What the correlation calculator does

Enter the covariance between two assets' returns and the standard deviation of each, and the calculator returns the correlation coefficient, along with the covariance and the product of the standard deviations so you can follow the working. A raw covariance is hard to judge because its size depends on the assets' volatility and units. Correlation rescales it to a range from -1 to +1, so you can see at once whether two assets are closely linked, loosely related or moving in opposite directions, and compare any pair.

How correlation is calculated

correlation = covariance / (standard deviation 1 × standard deviation 2)

The product of the standard deviations is the largest covariance the two assets could have if they moved perfectly together. Dividing the actual covariance by that maximum expresses the relationship as a fraction of the strongest possible link, which is why the result always lies between -1 and +1. The volatilities cancel out, so a pair of calm bonds and a pair of volatile growth stocks can share the same correlation even though their covariances look nothing alike.

Reading the result

Close to +1: the assets move almost perfectly together, so combining them adds little diversification.
Around 0: there is no meaningful linear relationship, which is useful for spreading risk.
Close to -1: the assets move in opposite directions, which can greatly smooth a combined portfolio.

Most real pairs fall in between. Two large stocks in the same market might show 0.7 or 0.8, while a stock and a government bond might sit near zero or turn slightly negative in a crisis.

Why correlation drives diversification

Holding two assets only reduces risk if they do not fall at the same time. Two investments with a correlation near +1 tend to drop together in a downturn. Two with low or negative correlation cushion each other, so the combined portfolio swings less than either alone. That is why portfolio builders study the correlation matrix of their holdings: an asset that behaves differently from everything else can lower total risk even if it is volatile on its own.

Try raising the covariance with the standard deviations fixed and watch the correlation move toward +1, or make the covariance negative and see it move toward -1.

Common pitfalls

A high correlation means two assets tend to move together, not that one causes the other; both may respond to a shared driver such as interest rates or the economic cycle. Correlations change over time and often rise toward +1 in market crises, exactly when diversification is needed most, so a figure measured in calm conditions can understate crash risk. And the sign matters as much as the size: -0.8 is as strong a relationship as +0.8, with opposite and often more useful behavior for a portfolio.

Use correlation alongside a volatility and portfolio-risk analysis to decide which assets to combine, and recheck it as market conditions change.

This article is general information only and is not financial advice.

About This Correlation Calculator

Use this correlation calculator to get an instant estimate based on the figures you enter. Adjust the inputs above to match your situation, or browse all our calculators to plan your next step.

Frequently asked questions

How does the correlation calculator work?

It divides the covariance between two assets by the product of their standard deviations. The result is the correlation coefficient, a standardised number between -1 and +1 that describes how strongly and in which direction the two assets move together. The tool also shows the covariance you entered and the product of the standard deviations so you can follow the calculation.

What is a correlation coefficient?

The correlation coefficient is a measure of the linear relationship between two variables, scaled to always fall between -1 and +1. A value of +1 means the two assets move perfectly in step, -1 means they move in perfectly opposite directions, and 0 means there is no linear relationship between them.

What is the difference between covariance and correlation?

Covariance tells you the direction of a relationship but its size depends on the units and volatility of the assets, so it is hard to interpret on its own. Correlation is covariance divided by the product of the standard deviations, which strips out those scales and leaves a clean number between -1 and +1 that you can compare across different pairs of assets.

Why does correlation matter for diversification?

Diversification works best when assets do not move together. A low or negative correlation means that when one asset falls, the other tends to hold up or rise, smoothing the overall portfolio. Combining assets with high positive correlation adds far less protection, because they tend to drop at the same time.

Can correlation be greater than 1?

No. By construction the correlation coefficient is always between -1 and +1. If your inputs produce a value outside that range, the covariance and standard deviations are inconsistent, because a valid covariance can never exceed the product of the two standard deviations.

Is my data kept private?

Yes. The calculation runs entirely in your browser. Nothing you enter is uploaded, stored, or shared with anyone.

About the author

Written and reviewed by

Taha Kheirandish

Economics student and independent researcher

Taha Kheirandish reads tax codes the way other people read maps — to find out where a system actually leads, not where it claims to go.

He is an economics student, and his work here is comparative by design. A pension deferral bonus in Quebec, a commuting allowance in Germany, a rent-increase ceiling in the Netherlands: each is a decision a government made about how money should move, and each reads differently once you set it beside eight others. He builds and checks these calculators across nine markets from primary sources — the regulation rather than a summary of it, the ministry’s own circular rather than a news item quoting it.

That is the editorial standard of the site as well as his habit. Every rate, threshold and bracket here carries the document it was read from and the date it takes effect, and gets re-checked when the law moves rather than when someone happens to notice.

He is a researcher, not a licensed adviser, and nothing on this site is personal financial advice. It is arithmetic done carefully with its sources shown — so that you can check it, and take it to someone who is.

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