Statistics Calculator

Correlation Calculator

Calculate Pearson’s correlation coefficient for paired numeric data and review r, R², sample size, direction, and an accessible strength description.

Free to useRuns in your browserClear formula & method

Enter your data

Correlation inputs

Use the fields below. Results update only when you select the calculate button.

The lists must contain the same number of paired observations in matching order.
Advertisement

What is a correlation calculator?

Pearson’s r summarizes the direction and strength of a linear relationship between two quantitative variables. It ranges from −1 for perfect negative linear association to +1 for perfect positive association.

Use this page for a transparent calculation, then compare the result with the Linear Regression Calculator when a different view of the same data would be useful.

How does this correlation calculator work?

The calculator centers both variables at their means, compares paired deviations, and scales the cross-product by the variation in each list.

Before interpreting spread or position, it can help to check the center with the Coefficient of Variation Calculator. Every tool states its assumptions so results can be reproduced.

r = Σ[(xᵢ − x̄)(yᵢ − ȳ)] / √[Σ(xᵢ − x̄)² × Σ(yᵢ − ȳ)²]

How to use this calculator

  1. Enter the requested numbers in the labeled fields.
  2. Review unit, sample, confidence, or test choices when shown.
  3. Select Calculate Correlation.
  4. Read the main result, supporting facts, and method note.
  5. Use Copy, Download, or Print when you need to keep the result; select Reset to start over.

If you edit any input after calculating, the old result is marked stale and hidden until you calculate again.

Advertisement

How should you interpret the result?

The sign gives direction and the absolute value gives linear strength. R² is the squared correlation, but it should not automatically be read as a causal effect.

For another useful perspective, open the Standard Deviation Calculator; it answers a related question without changing the values you entered here.

Assumptions and limitations

Correlation is sensitive to outliers, can hide curved relationships, and does not establish causation. Each x-value must be paired with the correct y-value.

Consider the Z-Score Calculator for a complementary summary and the Chi-Square Calculator when your question involves another statistical property. No single statistic describes every important feature of a data set.

Scope: Results are educational calculations, not a substitute for an appropriate study design, subject-matter expertise, or professional statistical review.

Frequently asked questions

Pearson’s r summarizes the direction and strength of a linear relationship between two quantitative variables. It ranges from −1 for perfect negative linear association to +1 for perfect positive association.
Use the labeled fields in the calculator and enter finite numeric values. The page validates missing, impossible, and mismatched inputs before showing a result.
r = Σ[(xᵢ − x̄)(yᵢ − ȳ)] / √[Σ(xᵢ − x̄)² × Σ(yᵢ − ȳ)²]
The sign gives direction and the absolute value gives linear strength. R² is the squared correlation, but it should not automatically be read as a causal effect.
Correlation is sensitive to outliers, can hide curved relationships, and does not establish causation. Each x-value must be paired with the correct y-value.
Yes. The calculator and BMI-style result panel are responsive for phones, tablets, laptops, and desktop screens.
No. Calculations run in your browser. This page does not require an account, and the entered values are not sent to a calculation server.
No. It is an educational tool for transparent calculations and quick checks. Important research, clinical, legal, financial, or policy decisions should use an appropriate study design and qualified review.

Sources and methodology

The formulas and cautions on this page are documented so the calculation can be checked against authoritative statistical guidance.

Advertisement