Pearson correlation calculator

Q: What is Pearson correlation?

Coefficient of linear relationship between two quantitative variables. Values from −1 to +1. Positive r — as one variable increases, the other tends to increase.

Q: How to interpret strength of relationship?

|r| 0.7 — strong. Thresholds are conventional and field-dependent.

Linear relationship of two variables. Enter X and Y — get r, r², p-value

Pearson correlation (r) — strength and direction of linear relationship between two variables. r from −1 to +1; also r² and p-value.

FAQ about Pearson correlation

Enter survey data

Variable X (numbers comma or space separated)

Variable Y (same number of values, same order)

Assumptions and limitations

Linear relationship; preferably normal distribution or large sample. Outliers strongly affect r.
Pairs (X, Y) must correspond to one object. Lengths of X and Y must match; extra values are dropped.

r and p-value

—

Enter X and Y

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Pearson correlation

What r measures

Strength and direction of linear relationship. r = 1 — straight line up, r = −1 — straight line down, r = 0 — no linear relationship (nonlinear may exist).

r²

Squared coefficient: share of variance in Y "explained" by X. r = 0.7 → r² = 0.49 — about 49% of Y variation is associated with X.

p-value

Significance of r differing from zero. At p < 0.05 the correlation is considered statistically significant (assuming assumptions hold).

Limitations

Correlation does not imply cause. Outliers distort r. For nonlinear relationships or ordinal variables other methods (Spearman, Kendall) may be better.

Pearson correlation calculation examples

1 Perfect positive relationship

X: 1, 2, 3, 4, 5. Y: 2, 4, 6, 8, 10. Y = 2×X — linear dependence.

Result: r = 1, r² = 1 — perfect positive relationship. All variance in Y is explained by X.

2 NPS and average order (5 customers)

X (NPS): 30, 50, 70, 45, 60. Y (avg order): 15, 22, 28, 18, 25.

Result: r positive, noticeable relationship (~0.95+). r² shows share of order variation linked to NPS — useful for reports.

3 Perfect negative relationship

X: 1, 2, 3, 4, 5; Y: 10, 8, 6, 4, 2. Y decreases as X increases.

Result: r = −1, r² = 1 — perfect negative relationship. The higher X, the lower Y.

4 Weak relationship (almost none)

X: 1, 2, 3, 4, 5, 6, 7; Y: 5, 2, 7, 1, 6, 3, 4 — almost random order.

Result: r close to 0, p likely > 0.05. No linear relationship (nonlinear may exist — check scatter plot).

5 Survey length and completion time

X — number of questions (10, 15, 20, 25, 30); Y — mean time in minutes (3, 5, 6, 8, 10).

Result: r positive and high — more questions, longer completion. r² shows what share of time can be predicted from survey length.

6 CES and NPS by customer

X — CES (1–5), Y — NPS (0–10) for the same customer. Enter pairs from export.

Result: positive r means easier interaction — higher NPS. Useful for "effort vs loyalty" reports.

Strength of relationship by |r|

|r|

Interpretation

< 0.3

Weak relationship

0.3 – 0.5

Moderate relationship

0.5 – 0.7

Noticeable relationship

> 0.7

Strong relationship

Thresholds are conventional and field-dependent. Check significance via p-value (at p < 0.05 correlation is considered significant).

Frequently asked questions about Pearson correlation

What is Pearson correlation?