Correlation Coefficient Calculator

1. Enter your x values, separated by commas.
2. Enter the matching y values, in the same order.
3. Read the correlation coefficient r, from minus 1 to plus 1.
4. See the covariance and the r-squared.

Here is what each result means:

The Pearson correlation coefficient, written r, measures how strongly two variables move together in a straight line. It ranges from minus 1 to plus 1. A value of plus 1 is a perfect upward line, minus 1 a perfect downward line, and 0 no linear link at all. So r near plus 0.9 means a strong positive relationship.

Correlation standardizes the covariance, so it has no units and can compare relationships on very different scales. It is a core tool for spotting associations in data, though a strong correlation shows only that two things move together, not that one causes the other.

It divides the covariance of the two variables by the product of their standard deviations.

1. Find how each value deviates from its mean.
2. Add the products of the paired deviations for the top.
3. Divide by the spread of each variable to standardize into r.

To fit an actual line to the same data, use the linear regression calculator, which shares these sums.

Find the correlation for x = 1, 2, 3, 4, 5 and y = 2, 4, 5, 7, 9.

Calculation: both variables rise together almost perfectly. Working through the formula gives r of about 0.99, a very strong positive correlation, and an r squared near 0.98. So nearly all of the variation lines up between x and y.

The size of r shows strength, and its sign shows direction.

Negative values mirror these, so minus 0.8 is a strong downward relationship. These bands are a guide, not strict cutoffs.

The two are related, but correlation is easier to compare.

Covariance shows the direction of the link but its size is hard to read. Correlation scales it into a clear range you can compare across data sets.

How Linear the Pattern Is

Correlation measures straight-line association. A strong curved link can still show a low r.

Outliers

A single far-off point can raise or lower r sharply, so check for stray values.

Range of the Data

A narrow range of values can hide a relationship and shrink r toward zero.

Spotting Relationships

See whether two variables tend to rise or fall together.

Comparing Links

Because r has no units, compare the strength of different relationships fairly.

Before Regression

Check that a linear model makes sense before fitting a line.

1. Reading Correlation as Causation

A strong r shows association, not that one variable causes the other.

2. Expecting R to Catch Curves

Pearson r measures straight-line links. A curved pattern can have a low r despite a clear relationship.

3. Ignoring Outliers

One stray point can swing r a long way. Inspect the data first.

4. Over-reading a Small Sample

A high r from just a few points can be down to chance. More data is more reliable.

5. Confusing R and R Squared

r ranges from minus 1 to plus 1; r squared is its square, from 0 to 1, and is always positive.

The correlation is exact for your data; only the displayed decimals are rounded.

It is a number, r, from minus 1 to plus 1 that measures how strongly two variables move together on a straight line. Plus 1 is a perfect upward line, minus 1 a perfect downward line, and 0 no linear link.

Find how each value deviates from its mean, add the products of the paired deviations, and divide by the spread of each variable. This standardizes the link into r, which this tool computes for you.

As a rough guide, an r above 0.7 in size is strong, 0.4 to 0.7 moderate, and below 0.4 weak. The sign shows direction, so minus 0.8 is a strong negative relationship.

No. A strong correlation shows two variables move together, but it does not prove that one causes the other. A third factor, or chance, can create the pattern.

Covariance shows the direction of a link but its size depends on the units, so it is hard to read. Correlation standardizes it into a range from minus 1 to plus 1, with no units.

Yes. Pearson r only measures straight-line links. A strong curved relationship, such as a U shape, can give an r near zero despite a clear pattern.

R squared is the square of the correlation, from 0 to 1. It gives the share of variation that lines up between the two variables. An r of 0.9 gives an r squared of 0.81.

At least two, but a handful of well-spread points is far more reliable. A high correlation from very few points may be down to chance.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Pearson correlation coefficient (Wikipedia).
• Correlation explained (Maths Is Fun).
• Covariance (Wikipedia).