CorrelLab

Correlation Coefficient Calculator

How strongly — and in which direction — two variables move together.

X values

Y values

Pearson correlation coefficient (r)

0.999

Ranges from −1 (perfect negative) to +1 (perfect positive)

What you entered

Pairs: 5

1
Mean of x
Σx ÷ 5= 3
2
Mean of y
Σy ÷ 5= 6.02
3
Pearson correlation coefficient r
Σ(x−x̄)(y−ȳ) ÷ √[Σ(x−x̄)² · Σ(y−ȳ)²]= 0.9987
4
Interpretation
|r| = 0.9987= strong positive correlation

Result

r: 0.999

r = 0.999 — a strong positive linear relationship between x and y.

Pearson correlation for paired datasets

Pearson's r measures the strength and direction of a straight-line relationship, from -1 for a perfect negative to +1 for a perfect positive.

X values	Y values	r	Interpretation
1, 2, 3, 4, 5	2, 4, 6, 8, 10	1.0000	Perfect positive
1, 2, 3, 4, 5	10, 8, 6, 4, 2	-1.0000	Perfect negative
10, 20, 30, 40, 50	50, 80, 95, 120, 140	0.9959	Very strong positive
1, 3, 5, 7, 9	2, 5, 4, 9, 8	0.8781	Strong positive

Row one is exactly 1.0000 because y is precisely twice x - r measures how well a straight line fits, not the slope of that line, so doubling and tripling both give the same perfect correlation. Two warnings the number cannot give you. Pearson only detects linear relationships: a perfect parabola can return an r near zero. And correlation is not causation, nor evidence of it - a strong r can come from a shared cause, from coincidence in a small sample, or from an outlier dragging the line. Always plot the data before trusting the coefficient.

What r actually measures

Pearson's r ranges from −1 (perfect inverse relationship) to +1 (perfect direct relationship), with 0 meaning no linear relationship at all — it only captures linear association, so a strong curved relationship can still score near zero.

Correlation isn't causation

A high correlation tells you two variables move together, not that one causes the other — ice cream sales and drowning rates correlate strongly because both rise in summer heat, not because one causes the other.

Frequently asked questions

Study hours vs exam scores: (2,65), (4,78), (5,82), (6,90), (8,95). How strong is the relationship?

r ≈ 0.99 — a near-perfect positive linear correlation. Each additional hour of study predicts roughly 5 more points. But correlation doesn't prove causation — stronger students may both study more AND score higher due to motivation.

How do I interpret the correlation value?

|r| < 0.3: weak. 0.3–0.7: moderate. > 0.7: strong. Sign indicates direction: positive = both rise together, negative = one rises as the other falls. r = 0 means no LINEAR relationship (there could still be a curved one).

How is Pearson's r different from Spearman's correlation?

Pearson measures linear relationships between raw values. Spearman measures monotonic relationships between ranks — it works for curved relationships and is robust to outliers. Use Pearson for continuous data with a linear trend; Spearman for ordinal data or when linearity is questionable. See the Spearman correlation calculator.

Can I use correlation to make predictions?

Correlation quantifies the strength of association, but for actual predictions (given x, what's the expected y?), use linear regression — it gives you the equation of the best-fit line. Use the linear regression calculator to find slope and intercept.