r Calculators Tool

Correlation Coefficient

Calculate Pearson’s correlation coefficient and R² for paired datasets. This page combines the live calculator with the underlying formula or method, a worked example and practical study notes.

Study Tools / Calculators / Correlation Coefficient
Study note: The interactive calculator below uses the same NexaMed Tools calculation engine as the main Study Tools hub, so this page is a search-friendly doorway into the same working calculator rather than a separate approximation.
Interactive calculator
Calculate Correlation Coefficient

What Is the Correlation Coefficient?

Calculate Pearson’s correlation coefficient and R² for paired datasets. The calculator is paired with the governing relationship so the numerical output stays connected to the concept you are studying.

Use this page to check worked examples, compare different inputs, and keep the meaning of each variable visible while practising.

Formula or Method

Formula / method
r = Σ[(x−x̄)(y−ȳ)] / √[Σ(x−x̄)² Σ(y−ȳ)²]

Pearson correlation standardizes covariance to a −1 to +1 scale and R² is r². Keep units and conventions consistent with the problem statement and with the options shown in the calculator.

How to Use the Calculator

  1. Read the input labels and enter the values requested by the problem or exercise.
  2. Check units, signs, angle mode, population/sample options, or other settings before calculating.
  3. Compare the result with the displayed formula or method and the worked example below.

Worked Example

Example: For Y = 2X with X = 1,2,3, r = 1 and R² = 1.

Common Mistakes

Why It Matters for Students

Correlation Coefficient is useful when a formula becomes a repeated part of problem solving. Use the page to verify a worked problem, inspect how changing an input changes the output, and keep the relationship itself visible rather than treating the calculator as a black box.

The numerical result is only as meaningful as the values, units and assumptions entered. For idealized physics and mathematics models, use the conventions specified in your course or problem statement.

Related NexaMed Study Tools

Standard Deviation
Compute population or sample variance and standard deviation from a dataset.
Mean / Median / Mode
Get mean, median, mode, minimum, maximum and range from one dataset.
Variance Calculator
Calculate population or sample variance with the corresponding standard deviation.
Covariance Calculator
Calculate population or sample covariance for paired datasets.
Scientific Calculator
A full scientific calculator with trigonometry, logarithms, powers, factorials, memory and history.

These pages are part of the same Study Tools system. For the complete collection, open the 2,420-tool NexaMed Study Tools hub.

Frequently Asked Questions

What is the correlation coefficient used for?
The Correlation Coefficient applies the relationship shown on this page to the inputs you provide. It is intended as a practical study and reference tool. Use the displayed method and keep the supplied units consistent.
What formula does the correlation coefficient use?
Pearson correlation standardizes covariance to a −1 to +1 scale and R² is r².
How do I use the correlation coefficient?
Enter the requested values, check the units or options, and calculate. Then compare the result with the formula, worked example and notes on the page. Use the displayed method and keep the supplied units consistent.
Calculation source: This page uses the NexaMed Prep Study Tools engine and the same tool definition used by the main interactive hub. Formula descriptions are presented for educational reference; follow the conventions, units and assumptions required by your course, textbook or examination.