What is Correlation?

Correlation measures refer to the degree to which two or more variables are related and change together. It defines the magnitude of the linear relationship between variables as well as the direction of that relationship.

How to use the correlation calculator?

The correlation calculator instantly computes correlation from paired data.

• Enter your first list of numbers (X values), separated by commas.
• Enter your second list of numbers (Y values), separated by commas.
• Important note: make sure both lists have the same number of items.
• After entering the value, click on “calculate”; in seconds, you will see the result.

Example 1: Strong Positive Correlation

1. X = 1, 2, 3, 4
2. Y = 1, 2, 3, 4
3. Number of pairs (n) = 4
4. Mean of X = 2.5
5. Mean of Y = 2.5
6. Deviation Products = 5
7. Sum of squared deviations X = 5
8. Sum of squared deviations Y = 5
9. Correlation formula: r = Σ(x-x̄)(y-ȳ) / √[Σ(x-x̄)² × Σ(y-ȳ)²]
10. r = 5 / √(5 × 5) = 1
11. Interpretation: Very strong positive correlation

Example 2: Strong Negative Correlation

1. X = -1, 5, 7, -9
2. Y = -2, 4, -6, 8
3. Number of pairs (n) = 4
4. Mean of X = 0.5
5. Mean of Y = 1
6. Deviation Products = -94
7. Sum of squared deviations X = 155
8. Sum of squared deviations Y = 116
9. Correlation formula: r = Σ(x-x̄)(y-ȳ) / √[Σ(x-x̄)² × Σ(y-ȳ)²]
10. r = -94 / √(155 × 116) = -0.701
11. Interpretation: Strong negative correlation

How does the correlation calculator work?

It measures linear association by comparing how X and Y deviate from their means. Values range from -1 to +1. The calculator converts the data to ranks, applies the correlation formula to those ranks, and finds a monotonic relationship.

Why use the MathCalc correlation calculator?

Get quick results: If you are finding correlation by hand, it can take time, especially when dealing with large numbers. This free MathCalc correlation calculator gives accurate results in seconds.

Example: Example: if you are finding a correlation between X = 2, 4, 6, 8, or Y = 2, 4, 6, 8. The calculator gives you an accurate result (positive correlation) in seconds.

Reduce Human Error

Manual math can lead to minor mistakes that cost you money or points. This tool provides proven formulas to reduce errors, and your results are always right. To avoid miscalculations, use the MathCalc correlation calculator.

Example: Example: if you are finding a correlation between X = 2, 3, 4, 5, or Y = 2, 3, 4, 5. The calculator gives you an accurate result (positive correlation) in seconds.

User-Friendly

The MathCalc correlation calculator has a simple interface. The result includes plain language interpretation. It is helpful for students.

Tips for the Best Result

• Make sure both lists have the same length.
• Always double-check your input.
• Remove extra values from lists.

FAQ

What is a correlation coefficient?

The correlation coefficient (r) is a number between -1 and +1. It measures how two variables move together. +1 is a perfect positive, -1 is the best negative, and 0 is no linear relationship.

Can I paste large data sets?

Yes! You can paste numbers separated by commas, spaces, or new lines. Make sure both lists have the same length.

What if my lists have different lengths?

You must provide paired data. Make sure that both lists have the same length.