Correlation Coefficient Calculator
You have two sets of numbers and want proof they move together. Type your paired data below and get the exact strength and direction of that relationship in seconds, with a chart that shows it plainly.
Step 1: Enter your paired data
| X value | Y value |
|---|
Scatter plot with trend line
Variance explained
Share of Y’s spread linked to X
What this means
To improve this result
What the correlation coefficient tells you
Pearson’s r is a single number between negative 1 and positive 1. It tells you two things at once: the direction two variables move in, and the tightness of that pattern. A number near positive 1 means both variables rise together. A number near negative 1 means one rises while the other falls. A number near zero means the two barely move together at all.
Finance and business teams use it to test a hunch before they act on it. Marketing spend and revenue, staff headcount and output, interest rates and loan demand: any pair of numbers can be tested this way before real money gets committed to a decision.
The formula, broken down
Pearson’s formula looks intimidating written in one line, but it only does two jobs: measure how the pairs move together, then divide by how much each variable spreads out on its own.
Take each pair, subtract its average, multiply the two results, then add every pair together. This shows whether X and Y tend to move together or apart.
Square and total the distance of every X from its average, do the same for Y, multiply those two totals, then take the square root. This is the natural spread of the two variables on their own.
A worked example
A small shop tracks monthly ad spend against monthly revenue over six months, in US dollars.
| Month | Ad spend | Revenue |
|---|---|---|
| 1 | 200 | 2,100 |
| 2 | 250 | 2,400 |
| 3 | 300 | 2,600 |
| 4 | 320 | 2,750 |
| 5 | 400 | 3,100 |
| 6 | 450 | 3,400 |
- 1. Average ad spend is $320. Average revenue is $2,725.
- 2. Subtract those averages from every value, then multiply each matching pair. Add every result together to get 218,000.
- 3. Square and total the ad spend distances (43,000), then do the same for revenue (1,108,750). Multiply those two totals and take the square root: about 218,340.
- 4. Divide 218,000 by 218,340. The result is r ≈ 0.998, a near perfect positive correlation.
An owner reading this result would treat ad spend as a strong predictor of that month’s revenue, while still checking for other causes such as a holiday season or a new product launch before locking in a marketing budget.
Frequently asked questions
A value close to positive 1 or negative 1 signals a tight, dependable relationship. A value near 0.7 or above (in either direction) is generally treated as strong in business and finance work, though the right cutoff depends on the field and the stakes of the decision.
No. Correlation only shows that two variables move together. A hidden third factor, or plain coincidence, can produce a high number even when neither variable causes the other.
Positive means both variables tend to rise or fall together. Negative means one tends to fall while the other rises, such as price and units sold in many markets.
A strong r gives you confidence a pattern exists, but it doesn’t hand you a prediction formula on its own. Pair it with our Linear Regression Calculator once you know a real relationship is there.
Small samples are sensitive to a single outlier. A pair far from the rest can swing r by a large margin. Aim for at least 20 to 30 pairs before you treat a result as trustworthy for a real decision.
Go further with your data
A correlation number is a starting point, not a full answer. Pair it with these tools to turn a pattern into a working forecast.