Statistics
Correlation Coefficient Calculator
Quantify the strength and direction of a linear relationship with Pearson’s r plus the supporting covariance and standard deviations.
Quantify linear association between paired lists with Pearson r and R².
Pearson correlation
r = Σ((x − x̄)(y − ȳ)) / [(n − 1) sₓ sᵧ]
Standard deviations sₓ and sᵧ come from the same datasets, so r stays bounded between −1 and 1 and highlights how tightly the paired values move together.
How to use
- Paste X values and Y values in the same order.
- Ensure each list has at least two numeric entries.
- Review r, R², covariance, and each sample standard deviation.
Example
Input: X = 12, 18, 25, 39; Y = 22, 32, 38, 55
Output: r ≈ 0.99, R² ≈ 0.98, Covariance ≈ 107.8
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Correlation Coefficient Calculator: correlation coefficient calculator, pearson r calculator, covariance calculator, correlation calculator online. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic — each one is a quick way to double-check your work or handle a related question without starting from scratch.
Deep dive & study plan
Correlation Coefficient Calculator: Finds Pearson r, covariance, and standard deviations for paired samples. It's built around correlation, pearson r, covariance, so you can go from a raw question to a checked answer without switching tools.
The math behind it: Standard deviations sₓ and sᵧ come from the same datasets, so r stays bounded between −1 and 1 and highlights how tightly the paired values move together. The core relationship is r = Σ((x − x̄)(y − ȳ)) / [(n − 1) sₓ sᵧ], shown above the calculator so you can see exactly how your inputs turn into the result.
To use it well: (1) Paste X values and Y values in the same order. (2) Ensure each list has at least two numeric entries. (3) Review r, R², covariance, and each sample standard deviation. Keep your units consistent as you go, and re-run a case you already know the answer to — it's the fastest way to catch a typo before it throws off a result you're relying on.
Worked example: entering X = 12, 18, 25, 39; Y = 22, 32, 38, 55 returns r ≈ 0.99, R² ≈ 0.98, Covariance ≈ 107.8. Try swapping in your own numbers next, especially a case you're unsure about, before you use this for something that matters.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Check at least one related calculator below — it's the fastest way to confirm your numbers still line up from a different angle.
FAQ & notes
How does this differ from regression?
Correlation measures strength of association only. If you also need slope and predictions, jump to the linear regression calculator.
Why does r sometimes report 0?
If one list has no variation (all values identical) the standard deviation is zero, so Pearson r cannot be computed and the calculator reports 0 as a neutral result.
What formula does the Correlation Coefficient Calculator use?
Standard deviations sₓ and sᵧ come from the same datasets, so r stays bounded between −1 and 1 and highlights how tightly the paired values move together.
How do I use the Correlation Coefficient Calculator?
Paste X values and Y values in the same order. Ensure each list has at least two numeric entries. Review r, R², covariance, and each sample standard deviation.