What is the Pearson correlation coefficient r?

Pearson r measures how closely two variables move in a straight line together. It ranges from −1 to +1: r near +1 means high X goes with high Y, r near −1 means high X goes with low Y, and r near 0 means no straight-line link. For example, hours studied versus exam score might give r = 0.92, a strong positive relationship; the tool computes it from the centered cross-products of your X and Y columns.

What range can r take, and what do the values mean?

r is always between −1 and +1 and cannot fall outside that band. A common reading (Evans, 1996) is: below 0.20 very weak, 0.20 to 0.40 weak, 0.40 to 0.60 moderate, 0.60 to 0.80 strong, and 0.80 and up very strong, applied to the absolute value. So r = −0.74 is a strong negative correlation, while r = 0.15 is very weak. The sign tells direction, the size tells tightness.

What is r² (the coefficient of determination)?

r² is simply r squared, and it tells you the share of variation in Y that the straight-line fit on X explains. If r = 0.80 then r² = 0.64, meaning 64 percent of the spread in Y is accounted for by X and the remaining 36 percent comes from everything else. It is handy because it converts an abstract correlation into a percentage you can quote, for instance saying advertising explains 64 percent of the sales swing.

Does a high correlation prove that X causes Y?

No. Correlation is not causation. Ice cream sales and drowning deaths rise together because both follow summer heat, not because dessert is dangerous. A high r only says the two numbers move in step; a hidden third factor, reverse causation, or pure coincidence can all produce it. To claim cause you need a controlled experiment or a strong causal argument, not just a large r value.

How do I read the strength of a correlation?

Look at the absolute value of r for strength and the sign for direction. r = 0.05 is essentially noise, r = 0.45 is a moderate positive trend, r = −0.88 is a very strong negative trend. Always glance at the scatter plot too: a single far-out point can inflate or hide r, and Pearson only catches straight-line patterns, so a clear curved relationship can still show r near zero.

What does the linear regression line add?

The regression line is the best straight-line fit, written y = ax + b, where a is the slope (how much Y changes per unit of X) and b is the intercept (Y when X is zero). With study hours and scores you might get y = 4.6x + 48, meaning each extra hour adds about 4.6 points. r tells you how good that line is; the line itself lets you predict Y for a new X within the range of your data.

Check whether study time really tracks grades

A student logs hours studied and the score on each of ten quizzes, then pastes the pairs to see r. An r of 0.88 confirms the effort is paying off in a strong, positive way; an r of 0.15 is a wake-up call that hours alone are not the lever and something about how the time is spent matters more. The regression line even estimates how many points one more study hour tends to buy.

Test if ad spend moves sales before the next budget

A marketer lines up monthly ad spend against revenue for the past year and pastes the twelve pairs. A strong positive r plus an r² of 0.70 is a defensible line in the budget meeting: roughly 70 percent of the sales swing tracks with spend. A weak r is just as useful, because it stops the team from pouring more money into a channel that is not actually pulling the numbers.

Screen variables in a research dataset

Before running a heavier model, a researcher pastes two columns to get a quick Pearson r and a scatter plot. The plot catches the things a single number hides: a lone outlier inflating r, or a clear curve that Pearson scores near zero because it only sees straight lines. It is a fast first pass that flags which pairs are worth a deeper look.

Show students what r looks like on a chart

A teacher demonstrates correlation by pasting a perfectly linear set (r = 1), then a scattered one (r near 0), then a negative set, and the scatter plot redraws each time. Seeing the points tighten around the regression line as r climbs turns an abstract formula into something students can point at, far stickier than memorizing the equation.

Correlation Coefficient Calculator — Pearson r, r² and Regression

Paste X,Y pairs → Pearson r, r², covariance, regression line and a scatter plot — runs entirely in your browser

Runs locally
Category Calculator
Best for Getting a realistic range before a purchase, plan, workout, or schedule decision.

Paired data (one X,Y pair per line)

Up to 5000 pairs. Each line: X then Y, separated by comma, space or tab. Decimals, negatives and 1.5e-3 all work.

Try a dataset

Pearson correlation r · 10 pairs

0.9974

Very strong · positive correlation — as X rises, Y tends to rise.

r² (coefficient of determination)

0.9948

99.5% of the variation in Y is explained by X.

Covariance (sample, n−1)

41.6111

Mean of X (x̄)

5.5

Mean of Y (ȳ)

73.1

Std dev of X (s)

3.02765

Std dev of Y (s)

13.7796

Linear regression (least squares)

Regression equation

y = 4.53939x + 48.1333

Slope (a)

4.53939

Intercept (b)

48.1333

Scatter plot

Show regression line

Correlation is not causation. A high r only means X and Y move together; it does not prove one causes the other.

Every X and Y stays in your browser tab. The numbers are computed locally and never uploaded or logged.

What this tool does

Free Pearson correlation coefficient calculator. Paste paired data, one X,Y pair per line, and read the Pearson r the moment you type. The tool reports r on the −1 to +1 scale, r² (the coefficient of determination, how much of Y's variation X accounts for), the sample covariance, and the mean and standard deviation of each variable. It then says in plain words whether the link is strong, moderate or weak and which direction it runs. Turn on the least-squares regression line to get the equation y = ax + b, with slope and intercept laid out, drawn straight over the scatter plot so you can see how tightly the points hug the trend. Every number is computed locally in JavaScript, so a class roster of grades or a quarter of sales figures never leaves the page. The share link reopens the same dataset and chart, which makes it easy to hand a result to a classmate or a colleague.

Tool details

Input: Text + Numbers; The page exposes text boxes, numeric controls, file pickers, or structured inputs depending on the tool.
Output: Live result + Copy + Preview; The result area focuses on usable output, with copy, download, or preview actions when supported.
Privacy: Browser-side processing; The main tool logic does not call an external API, so inputs normally stay in the current tab.
Save / share: Shareable URL state; Key settings are encoded in the URL so another person can reopen the same setup.
Performance budget: Initial JS <= 10 KB; No WASM budget is declared, keeping the tool quick to open on mobile.
Best fit: Calculator · Student; Category and role tags drive related tools, internal links, and quick fit checks.

How to use

1. Input

Paste or drop your content into the tool panel.
2. Process

Click the button. All processing is local in your browser.
3. Copy / Download

Copy the result or download to disk in one click.

How Correlation Coefficient Calculator fits into your work

Use it for fast estimates, comparisons, and planning numbers before you make the final call.

Calculation jobs

Getting a realistic range before a purchase, plan, workout, or schedule decision.
Comparing scenarios by changing one input at a time.
Turning rough assumptions into a number you can discuss.

Calculation checks

Double-check units, dates, rates, and rounding assumptions.
Treat health, finance, tax, and legal outputs as planning aids, not professional advice.
Save the inputs that produced an important result so you can reproduce it later.

Good next steps

These links move the current task into a more complete workflow.

Real-world use cases

Check whether study time really tracks grades
A student logs hours studied and the score on each of ten quizzes, then pastes the pairs to see r. An r of 0.88 confirms the effort is paying off in a strong, positive way; an r of 0.15 is a wake-up call that hours alone are not the lever and something about how the time is spent matters more. The regression line even estimates how many points one more study hour tends to buy.
Test if ad spend moves sales before the next budget
A marketer lines up monthly ad spend against revenue for the past year and pastes the twelve pairs. A strong positive r plus an r² of 0.70 is a defensible line in the budget meeting: roughly 70 percent of the sales swing tracks with spend. A weak r is just as useful, because it stops the team from pouring more money into a channel that is not actually pulling the numbers.
Screen variables in a research dataset
Before running a heavier model, a researcher pastes two columns to get a quick Pearson r and a scatter plot. The plot catches the things a single number hides: a lone outlier inflating r, or a clear curve that Pearson scores near zero because it only sees straight lines. It is a fast first pass that flags which pairs are worth a deeper look.
Show students what r looks like on a chart
A teacher demonstrates correlation by pasting a perfectly linear set (r = 1), then a scattered one (r near 0), then a negative set, and the scatter plot redraws each time. Seeing the points tighten around the regression line as r climbs turns an abstract formula into something students can point at, far stickier than memorizing the equation.

Common pitfalls

Treating a high r as proof of causation. r only says two variables move together; a lurking third factor or coincidence can drive that. The tool prints a "correlation is not causation" reminder under every result for exactly this reason.
Trusting r without looking at the scatter plot. Pearson only measures straight-line strength, so a clear curve can score r near zero, and one extreme outlier can push a near-zero r up to 0.7. Always read the chart alongside the number.
Confusing the sign with the strength. r = −0.9 is a very strong relationship, not a weak one; the minus sign means direction (X up, Y down), while the size 0.9 means it is tight. A small positive r like 0.1 is weak despite being positive.

Privacy

The whole calculation — Pearson r, r², covariance, each mean and standard deviation, the regression fit and the scatter plot — is plain JavaScript running in your browser tab. Your X and Y numbers are never uploaded and nothing about them is logged. One thing to know: the shareable link encodes your pasted data in the query string, so sending a "share link" writes those numbers into the recipient server's access log. If a dataset is confidential, use the copy button to share the computed results as text instead of pasting the URL.

FAQ

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Correlation Coefficient Calculator — Pearson r, r² and Regression

What this tool does

Tool details

How to use

1. Input

2. Process

3. Copy / Download

How Correlation Coefficient Calculator fits into your work

Calculation jobs

Calculation checks

Good next steps

Real-world use cases

Check whether study time really tracks grades

Test if ad spend moves sales before the next budget

Screen variables in a research dataset

Show students what r looks like on a chart

Common pitfalls

Privacy

FAQ

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