Calculadora de Correlação (Pearson r)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
r = Σ(xᵢ−x̄)(yᵢ−ȳ) / √(Σ(xᵢ−x̄)² · Σ(yᵢ−ȳ)²)
About this calculator
The Correlation Calculator (Pearson r) computes the Pearson linear correlation coefficient for up to 5 pairs of values (x, y). The coefficient r measures the strength and direction of the linear relationship between two variables, ranging from -1 to 1. Values near 1 indicate a strong positive correlation, near -1 a strong negative correlation, and near 0 no linear correlation. The formula used is: r = Σ(xᵢ−x̄)(yᵢ−ȳ) / √(Σ(xᵢ−x̄)² · Σ(yᵢ−ȳ)²), where x̄ and ȳ are the means of the variables.
To use the calculator, enter the x and y values in the provided fields. You can add up to 5 pairs. After filling, click 'Calculate' to obtain the r value. The result will be displayed with up to 4 decimal places. The tool also shows a basic interpretation of the coefficient, such as 'strong positive correlation' or 'weak negative correlation', based on the absolute value of r.
This calculator is useful in various fields such as statistics, social sciences, biology, and economics to analyze the relationship between two variables. For example, it can be used to check if there is a correlation between study hours and exam scores, or between temperature and energy consumption. It is important to remember that correlation does not imply causation: even if two variables are strongly correlated, it does not mean one causes the other.
Cautions: Pearson correlation is sensitive to outliers, which can distort the result. Additionally, it only measures linear relationships; non-linear relationships may not be detected. Finally, the calculator is limited to 5 pairs, making it suitable only for small datasets. For larger samples, specialized statistical software is recommended.
Frequently asked questions
What does an r value of 0 mean?
An r value of 0 indicates no linear correlation between the variables. It does not mean there is no relationship, only that it is not linear.
Can I use this calculator for more than 5 data pairs?
No, this calculator accepts a maximum of 5 pairs. For larger datasets, use statistical software like Excel, R, or Python.
What should I do if the data contains outliers?
Outliers can significantly affect the correlation coefficient. Consider removing them or using robust methods, such as Spearman's correlation.
Does Pearson correlation work for categorical data?
No, Pearson correlation is suitable only for continuous quantitative variables. For categorical data, use other tests like chi-square.
What is the difference between positive and negative correlation?
Positive correlation (r > 0) means that as x increases, y tends to increase. Negative correlation (r < 0) means that as x increases, y tends to decrease.