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Correlation Coefficient Calculator: Pearson and Spearman

This free correlation calculator measures how strongly two variables move together. It gives Pearson’s r, Spearman’s rank correlation, R squared, a plain-language strength and an approximate p-value.

By Debmedia Technologies LLP · Kolkata, India · Updated

What Is It and When Do You Need It?

Correlation shows whether two sets of numbers move together. Height and weight rise together, hours of study and errors may fall together, and ice cream sales and sunburn both rise in summer without causing each other.

Enter pairs and read Pearson and Spearman side by side.

How to Use This Tool

  1. Enter one pair per line.
  2. Press Calculate.
  3. Read r, rho and R squared.
  4. Compare the two measures to judge whether the link is straight or just consistent.

How the Calculation Works

Pearson r = (n Σxy − Σx Σy) ÷ √((n Σx² − (Σx)²)(n Σy² − (Σy)²)). Spearman rho is Pearson r computed on the ranks, with tied values given their average rank. The p-value comes from t = r × √((n − 2) ÷ (1 − r²)) on n − 2 degrees of freedom.

Worked Example

For the pairs (1, 1), (2, 4), (3, 9), (4, 16), (5, 25), Pearson r is 0.9811 and Spearman rho is 1, because the order matches exactly but the line is curved.

Common Uses

  • Research and school projects.
  • Business and marketing analysis.
  • Checking relationships in data.
  • Teaching statistics.

Tips and Common Mistakes

  • Plot your data as well.
  • A few points can give a misleadingly high r.
  • Use at least ten pairs for meaningful results.

Next, you may need the linear regression calculator, percentile calculator, confidence interval calculator, z-score calculator.

Everything runs in your browser. Nothing you type is uploaded, stored or sent to any outside service.

Frequently Asked Questions

A number from −1 to +1 that measures a straight-line link. +1 means a perfect rise together, −1 a perfect opposite move and 0 no linear link.
A correlation of the ranks. It measures whether the variables move in the same direction, even if the link is curved, and it is less affected by outliers.
No. Two things can move together because of a third factor or by chance.
The chance of seeing a correlation this strong from random data if there were really none. Small values, below 0.05, suggest a real link.

Disclaimer: results are calculated in your browser from the numbers you enter. Check important results before you rely on them for money, health, safety or legal decisions.