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Pearson correlation calculator

Measures the strength and direction of the linear relationship between two continuous variables. Returns r, r², and a t-based significance test.

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Your data

Two columns of equal length — values are paired by position (each case contributes one X and one Y). Rename X and Y to your variable names.

n = 0
n = 0
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When to use this

Use Pearson’s r when two continuous variables are measured on the same cases and you want to quantify how strongly they move together in a straight-line fashion — study time and exam score, age and reaction time, temperature and sales. r ranges from −1 (perfect negative) through 0 (no linear relationship) to +1 (perfect positive), and r² tells you the share of variance the variables have in common. The accompanying t-test asks whether the correlation in your sample is distinguishable from zero in the population.

Key assumptions

  • Each case contributes one X and one Y; pairs are independent across cases.
  • Both variables are interval or ratio scaled.
  • The relationship is approximately linear — always look at a scatterplot first.
  • For the p-value: bivariate normality, and no extreme outliers (a single outlier can manufacture or destroy a correlation).

Common mistakes

  • Inferring causation from correlation — r says nothing about direction or confounding.
  • Using Pearson on a clearly curved relationship; r only captures linear association (a perfect U-shape can give r ≈ 0).
  • Letting one outlier drive the result — inspect the scatterplot and consider Spearman’s ρ as a robustness check.
  • Interpreting a significant but tiny r (e.g. .08 in a huge sample) as practically meaningful.

Frequently asked questions

How large does r have to be?
Common benchmarks: |r| ≈ .10 small, .30 medium, .50 large. But fields differ — in psychology a .40 between two questionnaires is substantial, while instrument calibration may demand .95+. Report r, the sample size and the context.
What is the difference between r and r²?
r is the correlation coefficient (direction + strength); r² is the coefficient of determination — the proportion of variance in one variable linearly shared with the other. r = .50 means r² = .25, i.e. 25% shared variance.
When should I use Spearman instead of Pearson?
Use Spearman’s ρ when the data are ordinal (ranks, Likert items), when the relationship is monotonic but not linear, or when outliers distort Pearson’s r. We have a free Spearman calculator too.

Related free tools

Sample size calculatorSample size for two groupsEffect size (Cohen's d)Descriptive statisticsOne-sample t-testIndependent t-testPaired t-testz-table (standard normal)t-table (critical values)Chi-square table

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