Statistics calculator

Correlation Coefficient Calculator

Calculate Pearson correlation from five x-y data pairs.

Correlation guide

Read Pearson correlation as linear association, not proof of cause

Pearson r compares paired x-y observations and returns a value from -1 to 1. Values near 1 suggest a positive linear relationship, values near -1 suggest a negative linear relationship, and values near 0 suggest little linear association in the entered pairs.

A strong correlation can still be misleading when the sample is tiny, the relationship is curved, outliers dominate the result, or both variables move because of another factor. Plot the pairs, check units, and keep correlation separate from causation.

  • Use matched x-y pairs from the same observation.
  • Check for outliers before trusting r.
  • Use domain knowledge before inferring cause.
Statistics calculatorReview mean, median, mode, range, variance, and standard deviation before interpreting a relationship.Z-score calculatorStandardize a single value against a mean and standard deviation.Confidence interval calculatorEstimate uncertainty around a sample mean when sample size and spread are known.Sample size calculatorPlan a survey or study size before collecting the paired observations.
Formular = sum((x - mean x)(y - mean y)) / sqrt(sum(x - mean x)^2 sum(y - mean y)^2)

Formula

Pearson correlation

Correlation measures linear association, not causation.

r = sum((x - mean x)(y - mean y)) / sqrt(sum(x - mean x)^2 sum(y - mean y)^2)

Five x-y pairs can show positive, negative, or weak linear association.

FAQ6 common questions for this calculator.

FAQs

What does r near 1 mean?+

It means a strong positive linear relationship.

What does r near 0 mean?+

It means little linear relationship in the entered data.

How does the Correlation Coefficient Calculator calculate the result?+

For the Correlation Coefficient Calculator, it uses the Pearson correlation: r = sum((x - mean x)(y - mean y)) / sqrt(sum(x - mean x)^2 sum(y - mean y)^2). Five x-y pairs can show positive, negative, or weak linear association.

What information do I need to use the Correlation Coefficient Calculator?+

For the Correlation Coefficient Calculator, enter five x-y data pairs. Keep the units consistent with the calculator fields and compare your setup with the worked example on the page.

How accurate is the Correlation Coefficient Calculator?+

Correlation Coefficient Calculator calculates the selected statistic from the sample values provided. It uses the Pearson correlation, but missing data, outliers, sample bias, and distribution assumptions can affect what the result means.

What should I check before using the Correlation Coefficient Calculator result?+

For the Correlation Coefficient Calculator, check five x-y data pairs, sample definition, missing values, outliers, and rounding precision. A statistic can be numerically correct but still describe a weak sample.

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Statistics guide

How to use the Correlation Coefficient Calculator

Calculate Pearson correlation from five x-y data pairs. The page also explains the pearson correlation and shows a practical example: Five x-y pairs can show positive, negative, or weak linear association.

  1. 1

    Enter your details

    Enter five x-y data pairs, then complete any other fields shown in the calculator.

  2. 2

    Check the calculation

    Review the result alongside the pearson correlation: r = sum((x - mean x)(y - mean y)) / sqrt(sum(x - mean x)^2 sum(y - mean y)^2).

  3. 3

    Compare scenarios

    Change one or more inputs to see how they affect the correlation Coefficient Calculator result before you use the estimate.