Correlation Calculator
Pearson product-moment linear correlation of paired observations. No significance test or causation claim.
In short
Pearson product-moment linear correlation of paired observations. No significance test or causation claim.
Formula: r = Σ((xᵢ − x̄)(yᵢ − ȳ)) ÷ √(Σ(xᵢ − x̄)² × Σ(yᵢ − ȳ)²).
What this calculator does
Pearson product-moment linear correlation of paired observations. No significance test or causation claim. Formula, worked example, sources, FAQs and limitations included.
Use it to turn Observations, Paired values y into a checked result you can compare, copy, or rerun with different assumptions.
The page shows the formula, a numeric worked example, and the assumptions that affect this statistics calculation.
Inputs and what they mean
- Observations
- — text value.
- Paired values y
- — text value.
How to use it
- Enter each value in the unit shown next to the box (use the unit converter first if your numbers are in other units).
- Check the breakdown to see every intermediate step.
- Read the limitations before relying on the result.
Formula
Methodology type: scientific equation.
Methodology: NIST Pearson product-moment linear correlation, not Spearman rank correlation.
No p-value or normal-distribution inference is calculated. Nonlinear association may exist even when r is near zero.
r = Σ((xᵢ − x̄)(yᵢ − ȳ)) ÷ √(Σ(xᵢ − x̄)² × Σ(yᵢ − ȳ)²).
Inputs used: Observations, Paired values y.
Worked example
Pearson r
- Sxy = 4, Sxx = 2, Syy = 8; r = 4 ÷ √16 = 1.
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
Limitations and assumptions
- Paired finite values; sensitive to outliers.
- No significance test or causation claim.
- For education and operational analysis only. No diagnosis, treatment recommendations, prescribing, dosing instructions, or reimbursement entitlement. Scientific calculations require appropriate laboratory verification; operational estimates do not replace local clinical, safety or financial policies.
- The result depends on the values you enter for this correlation calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.
Reference: NIST
Last reviewed:
Common questions
Is this Spearman correlation?
No. Pearson r uses numeric values rather than ranks.
Why reject a constant list?
Its variance is zero, so the correlation denominator is zero. Check the formula, example, and limitations on this page before using the result for a real statistics decision.
Does r = 0 mean no relationship?
No. It indicates no linear correlation; a nonlinear relationship may remain.
How do I use the Correlation Calculator?
Enter the required values for Observations, Paired values y. The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.
What formula does the Correlation Calculator use?
r = Σ((xᵢ − x̄)(yᵢ − ȳ)) ÷ √(Σ(xᵢ − x̄)² × Σ(yᵢ − ȳ)²). The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone.
Can the Correlation Calculator be used for exact decisions?
Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.
Sources
Method based on NIST.
Cite this page
Free Calculator. (2026, October 23). Correlation Calculator. https://freecalculator.tech/tools/pearson-correlation-calculator
"Correlation Calculator." Free Calculator, 23 Oct. 2026, https://freecalculator.tech/tools/pearson-correlation-calculator.
Correlation Calculator — Free Calculator, https://freecalculator.tech/tools/pearson-correlation-calculator
Related tools
Weighted arithmetic mean using your explicit nonnegative weights. Scientific equation with no inferred weighting scheme.
Unweighted middle ordered observation or average of the two middle values. Scientific descriptive statistic.
Estimated standard error of mean s/sqrt(n) for independent observations. Distinct from individual observation spread.
Two-sided Student t interval for a population mean with unknown variance. Enter confidence level explicitly; assumptions stated.
Standardized score from your entered mean and standard deviation. No normal distribution or medical risk inferred.
Absolute reference-relative error using the accepted reference magnitude. Zero reference is undefined.