Statistics
Pearson Correlation Coefficient Calculator
Calculate Pearson's correlation coefficient online to understand the linear relationship between two datasets. Visualize data with an interactive scatter plot.
Enter Your Data Sets
Input your datasets below, with values separated by commas. Ensure both datasets have the same number of values.
Correlation Result
Pearson Correlation Coefficient (r):
Data Visualization
Understanding Pearson Correlation Coefficient
The Pearson correlation coefficient, denoted as \( r \), measures the strength and direction of a linear relationship between two variables. It ranges from -1 to +1.
- +1: Perfect positive correlation. As one variable increases, the other tends to increase.
- 0: No linear correlation. Changes in one variable are not related to changes in the other.
- -1: Perfect negative correlation. As one variable increases, the other tends to decrease.
The formula for Pearson correlation coefficient is:
$$ r = \frac{\sum_{i=1}^{n}(x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i - ar{x})^2} \sqrt{\sum_{i=1}^{n}(y_i - \bar{y})^2}} $$
Learn more about Pearson correlation coefficient on Wikipedia.
Frequently Asked Questions
What is the Pearson Correlation Coefficient Calculator?
The Pearson Correlation Coefficient Calculator is an online Statistics calculator. You enter your values, and it returns the answer with the steps shown so you can follow along.
How accurate is the Pearson Correlation Coefficient Calculator?
The solver uses a math engine that avoids the floating-point rounding errors you get from most hardware calculators. For typical homework and professional calculations, the results will match what you would get by hand.
Can I use the Pearson Correlation Coefficient Calculator for professional Statistics projects?
Yes. The math behind it is standard Statistics, so the results are reliable for professional use. That said, always double-check that your inputs are in the right format before relying on the output.
Why use the Pearson Correlation Coefficient Calculator instead of calculating by hand?
Manual calculation is slow and error-prone, especially with multiple steps. This tool does the arithmetic for you and shows each step, so you can catch mistakes before they carry forward.
How do I format my inputs for the Pearson Correlation Coefficient Calculator?
Type your numbers into the input fields. Leave out units and symbols unless a field specifically asks for them. The solver handles the rest.