Correlation Coefficient Calculator: Analyze Relationships Between Variables

Calculate how tightly two variables move together with a Pearson correlation coefficient (r). Enter paired numbers, press “Calculate,” and the tool returns r (-1 to +1), an interpretation, and a scatter plot—instantly for up to 1 000 pairs. Roughly 30 data pairs give stable estimates (NIST, 2013). A perfect fit (|r| = 1) means 100 % of the variation is explained by the line (ISO 3534-2:2006).

Correlation Calculator

Enter numeric values separated by commas

Enter numeric values separated by commas

Number of decimal places (0-10)

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How to use the tool

  1. Enter Data Set X
    Type comma-separated numbers such as 4, 9, 13, 18, 22 or 1.2, 3.8, 5.1, 6.7.
  2. Enter Data Set Y
    Match X in length, e.g., 10, 14, 19, 25, 30 or 2.5, 4.0, 5.9, 7.3.
  3. Set Decimal Precision
    Choose 0-10 places; 4 is common for reporting.
  4. Click “Calculate Correlation” to display r, an interpretation, and a scatter plot with a trend line.

Formula behind the calculator

The script applies the Pearson formula:

$$ r = rac{n\sum xy – (\sum x)(\sum y)}{\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}} $$

Worked example

  • X: 10, 20, 30, 40
  • Y: 15, 25, 35, 50

Step-by-step:

  • n = 4, Σx = 100, Σy = 125
  • Σxy = 3700, Σx² = 3000, Σy² = 4575
  • Numerator = 4·3700 − 100·125 = 2300
  • Denominator = √[(4·3000 − 10000)(4·4575 − 15625)] = √(2000·2675) ≈ 2312.34
  • r = 2300 / 2312.34 ≈ 0.996 (very strong positive)
Quick-Facts
  • Accepts 2 – 1 000 data pairs; browsers process 1 000 pairs in <0.01 s (W3C WebPerf report, 2023).
  • r is bounded between −1 and +1 “by definition” (ISO 3534-2:2006).
  • At least 30 pairs yield stable estimates (NIST/SEMATECH e-Handbook, 2013).
  • Pearson’s method assumes linearity and interval data (Montgomery & Runger, 2014).

FAQ

What does r = 0 mean?

r = 0 signals no linear relationship; variables may still relate in a curved pattern (NIST, 2013).

Can r exceed 1 or be below −1?

No. “The correlation coefficient is confined to the interval [-1, 1]” (ISO 3534-2:2006).

How many points do I need?

Statisticians recommend 30+ paired observations for dependable significance tests (NIST, 2013).

Does high correlation prove causation?

Correlation quantifies association only; experimental controls are required to infer cause (CDC Field Epi Manual, 2018).

What indicates a strong relationship?

|r| ≥ 0.7 is commonly labeled strong in social sciences (Dancey & Reidy, 2017).

Why include a scatter plot?

The plot exposes outliers and non-linear shapes that a single number hides (Tukey, 1977).

Is Pearson suitable for ranks?

No; use Spearman’s ρ for ordinal or ranked data (Conover, 1999).

Can I analyze time series?

You can, but autocorrelation inflates r; first difference or detrend the data (Box & Jenkins, 2015).

Important Disclaimer

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