Correlation Coefficient Calculator: Pearson r & Spearman

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Formula at a glance

Correlation Calculator: Pearson r — r = Σ(x − x̄)(y − ȳ) / √(Σ(x − x̄)²·Σ(y − ȳ)²). Example: Six paired values → Pearson correlation r: 0.87831007 — How the Correlation Calculator works: Pearson r — r = Σ(x − x̄)(y − ȳ) / √(Σ(x − x̄)²·Σ(y − ȳ)²)

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📘 About the Correlation Coefficient Calculator

The correlation coefficient r measures the strength and direction of a straight-line relationship between two variables, from −1 (perfect negative) through 0 (none) to +1 (perfect positive). r² gives the share of the variation in Y explained by X. Spearman’s ρ does the same with ranks, for relationships that rise steadily but not in a straight line.

Paste the X and Y values in matching order. The calculator gives Pearson’s r, r², Spearman’s ρ, the covariance, a plain-English strength rating and a t-test of whether the correlation differs from zero.

🧮 Formula

Pearson r

r = Σ(x − x̄)(y − ȳ) / √(Σ(x − x̄)²·Σ(y − ȳ)²)

Significance

t = r√(n − 2)/√(1 − r²), df = n − 2

✏️ Worked examples

Six paired values

You enter
X values	1, 2, 3, 4, 5, 6
Y values (same order)	2, 4, 5, 4, 5, 7

You get
Pearson correlation r	0.87831007
Strength	Strong positive linear relationship
r² (coefficient of determination)	0.771429 — 77.14% of the variation in Y is explained by X
Spearman rank correlation ρ	0.85331034
Covariance (sample)	2.7
Significance (t-test, df = 4)	t = 3.67423, p = 0.0213116 — significant at 5%
Pairs n	6

r = 0.87831007.

Study hours vs marks

You enter
X values	2, 4, 6, 8, 10
Y values (same order)	55, 62, 70, 78, 88

You get
Pearson correlation r	0.99792439
Strength	Very strong positive linear relationship
r² (coefficient of determination)	0.995853 — 99.59% of the variation in Y is explained by X
Spearman rank correlation ρ	1
Covariance (sample)	41
Significance (t-test, df = 3)	t = 26.8408, p = 0.00011348 — significant at 5%
Pairs n	5

r = 0.99792439.

🧭 How to use this calculator

What you enter

X valuesSeparate numbers with commas, spaces or new lines.
Y values (same order)

What you get

Pearson correlation r
Strength
r² (coefficient of determination)
Spearman rank correlation ρ
Covariance (sample)
Significance (t-test, df = 4)
Pairs n

❓ Frequently asked questions

What is a strong correlation?

Roughly |r| ≥ 0.7 is strong, 0.5–0.7 moderate, 0.3–0.5 weak and below 0.3 very weak — but it depends on the field.

Does correlation mean causation?

No. Two variables can move together because of a third factor or by chance. Experiments are needed to show cause.

When should I use Spearman instead of Pearson?

When the data are ranks, have outliers, or the relationship is monotonic but curved.

r Correlation Coefficient Calculator (Pearson r & Spearman ρ)