Correlation Calculator

Pearson correlation coefficient and interpretation

Pearson correlation ranges from −1 to 1 and has no measurement unit. Its square describes the strength of this linear association in the supplied pairs; neither output establishes causation.

To combine values with explicitly unequal weights, use the Weighted Average Calculator and follow its own input conventions.

The formula

Center each column, sum paired deviation products, and normalize by both columns’ deviation magnitudes. Both columns must vary; constant inputs make the denominator zero.

How to use this calculator

1. Enter one x, y pair per line with a comma or space between the two values.
2. Preserve the original pairings and provide at least two rows.
3. Read Pearson r and its square while checking for outliers and nonlinear patterns in the underlying data.

Correlation input conventions

Each row represents one paired observation. Preserve the pairing when entering data; sorting one column independently invents a different relationship. Pearson’s coefficient is unitless and ranges from −1 to 1. Positive values indicate an upward linear association and negative values a downward one. A coefficient near zero can still coexist with a strong curved relationship.

Interpreting pearson correlation coefficient

Correlation does not establish causation, remove confounding, or assess sampling bias. Extreme observations can substantially change the coefficient, so examine the underlying pairs before reporting a summary. A constant column makes the denominator zero and its correlation undefined. Squared correlation is reported as a descriptive companion; it is not a general percentage of causal influence or proof that a model fits every part of the data.

Assumptions & limitations

What this calculation assumes

• Rows remain paired and both columns have nonzero variation.

What to keep in mind

• Pearson correlation only; no rank correlation, significance test, or causal inference.

Common questions