Correlation Coefficient Calculator
Find the Pearson correlation between two datasets.
Results update as you type.
How it works
The correlation coefficient measures how strongly two variables move together, and this calculator computes it from your data. You enter two lists of numbers, the paired x and y values, and it returns the Pearson correlation coefficient r and the sample size. Pearson's r quantifies the strength and direction of the linear relationship between the two variables on a scale from negative one to positive one. A value near positive one means a strong positive relationship, as one variable rises the other tends to rise; near negative one means a strong negative relationship, as one rises the other falls; and near zero means little or no linear relationship. Values in between indicate weaker relationships, and rough guidelines call an absolute value above 0.7 strong, around 0.3 to 0.7 moderate, and below 0.3 weak, though interpretation depends on the field. The calculator computes r from the sums of the values, their products, and their squares, using the standard formula. Correlation is widely used in statistics, science, economics, and data analysis to detect and measure associations, such as between study time and grades or advertising and sales. A crucial caution: correlation does not imply causation; a strong correlation shows the variables move together but not that one causes the other, which could be coincidence or a third factor. Also, r only captures linear relationships and can miss curved patterns. Enter matched x and y values to compute the correlation coefficient.
r = (nΣxy − ΣxΣy) / √((nΣx² − (Σx)²)(nΣy² − (Σy)²))
The Pearson correlation coefficient r measures the strength and direction of the linear relationship between two variables. It is computed from the sums of the x and y values, their products, and their squares. The result ranges from −1 (perfect negative) through 0 (none) to +1 (perfect positive correlation).
Source:Statistics
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Worked example
How to use this calculator
- 1
Enter your values
Enter x values (comma-separated) and y values (comma-separated).
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Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Correlation coefficient (r) updates instantly as you type — no button to press.
Frequently asked questions
What does the correlation coefficient measure?
The Pearson correlation coefficient, r, measures the strength and direction of the linear relationship between two variables. It ranges from negative one to positive one: positive values mean the variables rise together, negative values mean one rises as the other falls, and values near zero mean little linear relationship. It does not measure non-linear patterns.
What is a strong correlation?
As a rough guide, an absolute r above 0.7 is often considered strong, between 0.3 and 0.7 moderate, and below 0.3 weak, though the interpretation depends heavily on the field of study. A value of exactly 1 or negative 1 indicates a perfect linear relationship, while 0 means no linear association at all.
Does correlation imply causation?
No. This is a critical point: a strong correlation shows two variables move together, but not that one causes the other. The relationship could be coincidental, or both variables could be driven by a third, hidden factor. Establishing causation requires controlled experiments or careful analysis beyond correlation alone. Always interpret correlation cautiously.
What are the limitations of Pearson's r?
Pearson's r only captures linear relationships, so it can be near zero even when a strong curved (non-linear) relationship exists. It is also sensitive to outliers, which can distort the value, and it assumes the data are roughly interval-scaled. For non-linear or rank-based relationships, other measures like Spearman's correlation may be more appropriate.
How do I enter my data?
Enter your paired data as two comma-separated lists, one for the x values and one for the y values, with the values in matching order so each x pairs with its corresponding y. The lists should have the same number of values, at least two. The calculator parses the numbers and computes the correlation from all valid pairs.