Pearson Correlation Calculator

The Pearson correlation coefficient, written as r, measures how strongly two numeric variables move together in a straight line relationship. This calculator takes two lists of paired numbers, your x values and your y values, and returns r along with r-squared, the proportion of variation in one variable explained by the other. The value of r always sits between minus one and plus one. A value near plus one means that as x rises y tends to rise too, a value near minus one means y tends to fall as x rises, and a value near zero means there is little straight line relationship. Behind the scenes the tool divides the covariance of x and y by the product of their standard deviations, which is the same as summing the products of the centred values and scaling by the spread of each list. New Zealand students, analysts, scientists, and businesses use correlation to explore links such as advertising spend against sales, temperature against energy use, or study time against marks, before deciding whether a deeper model is worth building. To use it well, enter the same number of values in each list and keep the pairs in matching order, because each x must line up with its y. Remember that correlation is not causation, so a strong r tells you the two move together but not that one causes the other. Watch for outliers and curved patterns, since a single extreme point can inflate or hide a relationship and r only captures straight line links. Plot your data alongside r whenever you can to confirm what the single number is really telling you.

r = sum((x - xbar)(y - ybar)) / sqrt(sum(x - xbar)^2 * sum(y - ybar)^2). r-squared = r * r.