# Pearson Correlation Calculator

Calculate Pearson r, r squared, covariance, and confidence interval for paired numeric data

> Canonical page: https://elysiatools.com/en/tools/pearson-correlation-calculator

- **Category:** Math & Numbers

- **Keywords:** pearson correlation, pearson r, r squared, linear correlation, statistics, regression

## Overview

Calculate Pearson's product-moment correlation coefficient.

Pearson r measures linear association between two numeric variables on a scale from -1 to 1. The result also includes r squared, covariance, an optional Fisher confidence interval, and the least-squares regression line.

Use this tool when you specifically need linear correlation rather than rank-based correlation.

## Inputs

- **Data Pairs** (textarea): One pair per line: 1, 52 2, 57 3, 63 4, 68 5, 74
- **X Values Optional** (text): Alternative: 1, 2, 3, 4, 5
- **Y Values Optional** (text): Alternative: 52, 57, 63, 68, 74
- **Decimal Places** (number)
- **Confidence Level** (number)
- **Include Regression Line** (checkbox)

## When to use

- When you need to measure the strength and direction of a linear relationship between two continuous numeric variables.
- When evaluating the predictive power of a linear regression model using the R-squared value.
- When determining if two sets of numeric data move together, such as comparing study hours to test scores or marketing spend to revenue.

## How it works

- Enter your paired numeric data into the main text area, with one pair per line separated by a comma.
- Alternatively, paste your X and Y values into their respective separate input fields as comma-separated lists.
- Adjust the decimal places, confidence level, and toggle the regression line calculation as needed.
- The tool processes the data and outputs a JSON result containing the Pearson r, R-squared, covariance, and regression formula.

## Use cases

- Academic researchers analyzing the correlation between environmental factors and biological measurements.
- Financial analysts comparing the historical price movements of two different assets to assess market correlation.
- Educators evaluating the relationship between student attendance rates and final exam performance.

## Frequently asked questions

### What does a Pearson r value of 1 or -1 mean?

A value of 1 indicates a perfect positive linear relationship, while -1 indicates a perfect negative linear relationship. A value of 0 means there is no linear correlation.

### What is the difference between Pearson r and R-squared?

Pearson r measures the strength and direction of the linear relationship. R-squared represents the proportion of variance in the dependent variable that can be explained by the independent variable.

### Can I input X and Y values separately?

Yes, you can either paste paired data (X, Y) on each line in the primary input or use the dedicated X Values and Y Values fields for comma-separated lists.

### What is the Fisher confidence interval?

It is a statistical range that estimates the true population correlation coefficient based on your sample data and selected confidence level (e.g., 95%).

### Does this tool calculate the regression line?

Yes, if the 'Include Regression Line' option is checked, the tool calculates the least-squares regression line equation alongside the correlation metrics.

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