Correlation Calculator (Pearson r)
Measure how strongly two variables move together. Paste paired X and Y values in the same order.
Learn how to calculate it yourselfEnter your values
Results update as you type.
How to enter your data
Enter your data as two matching lists of numbers, one list for each thing you are measuring. Type or paste the numbers with a comma or a new line between each one. Make sure both lists have the same number of values and are in the same order, so the first number in one list pairs with the first number in the other.
Correlation (r)
Check your inputs
Enter valid values to see your result. Use the field hints or open the data guide for help.
The Pearson Correlation Calculator measures how strongly two sets of numbers move together, for example hours studied and exam marks. It gives you a single number between -1 and +1: a positive number means the two things tend to rise together, a negative number means one goes up while the other goes down, and a number near zero means there is little or no straight-line link. It shows a connection, but it does not prove that one thing causes the other.
Calculate it yourself
Example: paired observations are (1, 2), (2, 4) and (3, 3). Keep the X and Y values paired.
Follow this worked example, then repeat the steps with your own numbers.
Find the two means
Mean X = (1 + 2 + 3) ÷ 3 = 2; mean Y = (2 + 4 + 3) ÷ 3 = 3Subtract each mean
X deviations = −1, 0, 1; Y deviations = −1, 1, 0Sum products and squares
Sxy = (−1 × −1) + (0 × 1) + (1 × 0) = 1; Sxx = 1 + 0 + 1 = 2; Syy = 1 + 1 + 0 = 2Divide the cross-product by the scale of the data
r = Sxy ÷ √(Sxx × Syy) = 1 ÷ √(2 × 2) = 0.5; R² = 0.5² = 0.25
This is a small teaching example. Pearson’s r describes a linear association; it does not establish causation and can be strongly affected by outliers.
Check your answer in the calculatorBuilt into PaperSurvey.io
Select two numeric questions to measure how their answers vary together within the same respondents.
Where it is used
- Teachers: A teacher checks whether the number of hours pupils spend studying is linked to the marks they get on a test.
- Café and shop owners: A café owner sees whether hotter days go together with higher cold-drink sales across the past month.
- HR staff: An HR officer looks at whether staff satisfaction scores rise or fall with the number of years people have worked at the company.
Interpreting r
Pearson’s r ranges from −1 to +1. Values near +1 mean the two variables rise together, near −1 mean one rises as the other falls, and near 0 mean little linear relationship. Correlation does not imply causation.
When should you use it?
Use this calculator when you have two numbers recorded for each person or item and you want to know if they are linked. For example, for each pupil you might have hours studied and a test score, or for each day you might have the temperature and the number of drinks sold. It only works with numbers that can go up or down, like age, price, score, or count. It is not the right tool for yes or no answers, categories, or a single list of numbers on its own.
What does the result mean?
The result is one number between -1 and +1, often called r. A value near +1 means a strong link where both rise together. A value near -1 means a strong link where one rises as the other falls. A value near 0 means almost no straight-line link. A common guideline treats about 0.1 as a weak link, about 0.3 as moderate, and 0.5 or higher as strong. The plus or minus sign tells you the direction, and the size tells you the strength.
Mistakes to avoid
Do not assume a link means one thing causes the other. Ice cream sales and sunburn rise together, but ice cream does not cause sunburn; hot weather drives both. Keep your two lists in the same order so each pair belongs to the same person or item, and make sure both lists are the same length. Watch out for one very unusual value, as a single odd number can push the result up or down. Finally, a result from only a handful of pairs is not very reliable.
How to use this calculator
- Collect your paired numbers, so you have two measurements for each person or item, such as hours studied and test score.
- Type or paste the first measurement into the first list and the matching second measurement into the second list, keeping them in the same order.
- Separate each number with a comma or a new line, and check that both lists have the same number of values.
- Read the result: look at the plus or minus sign for the direction, and how close it is to 1 or -1 for the strength of the link.
Worked example
Imagine five pupils. Their hours studied were 1, 2, 3, 4, and 5, and their test scores were 50, 55, 65, 70, and 80. Enter the hours in one list and the scores in the other, in the same order. The calculator returns about 0.99, a very strong positive link, meaning pupils who studied more tended to score higher.
Frequently asked questions
What do I type in each box?
Type two lists of numbers, one for each thing you are measuring. The two lists must be paired, so the first number in one list matches the first number in the other, and both lists must have the same count of numbers.
Where do I get these numbers?
They usually come from your own records, such as survey answers, a spreadsheet, sales figures, or test scores. If you collect surveys with PaperSurvey, you can pull the two columns of numbers straight from your results.
What does the final number mean?
It shows how strongly the two things move together. Closer to +1 or -1 means a stronger link, and closer to 0 means little or no link. The plus or minus sign tells you the direction.
What counts as a strong result?
A widely used guide says about 0.1 is weak, about 0.3 is moderate, and 0.5 or higher is strong. The same sizes apply to negative values, so -0.6 is also a strong link.
Does a link mean one thing causes the other?
No. The calculator only shows that two things move together, not why. Something else may be causing both, so treat the result as a clue, not proof of cause.
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