Correlation Coefficient Calculator

Pearson’s correlation coefficient, written r, is a single number from −1 to +1 that summarizes how tightly two variables follow a straight line together. The sign gives the direction; the magnitude gives the strength.

The computing formula needs only five sums and the count of pairs — no means or deviations required.

1. 1

   Pair the values and find n

   Line up each x with its matching y. Count the pairs to get n. Both lists must be the same length.

   n = number of (x, y) pairs
2. 2

   Compute the five sums

   Add up the X values, the Y values, each product xy, and the squares x² and y².

   Σx, Σy, Σxy, Σx², Σy²
3. 3

   Build the numerator and denominator

   The numerator captures how X and Y vary together; the denominator scales it by how much each varies on its own.

   num = n·Σxy − Σx·Σy den = √((n·Σx² − (Σx)²)(n·Σy² − (Σy)²))
4. 4

   Divide to get r

   Divide the numerator by the denominator. The result is r, always between −1 and +1.

   r = num ÷ den

Textbooks show two equivalent forms. The computing form (top) is easiest by hand; the definitional form (bottom) shows what r really is — covariance divided by the product of the standard deviations.

The same procedure produces a positive, negative, or near-zero coefficient depending on how the data move together. Each tab computes r from real numbers.

There is no universal cutoff, but these widely taught bands turn an abstract r into a verdict. They apply to the absolute value, so they hold for negative correlations too.

Drag the slider to any value of r to read off its strength and direction instantly.

One number that screens for relationships across science, finance, and machine learning.

r is powerful but easy to misread. These are the traps that catch people most often.

The Pearson r on this page is the most common coefficient, but it has close relatives for different situations.

Common questions