Spearman Correlation Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/10/2026
The Spearman correlation coefficient measures the strength of a monotonic (not necessarily linear) relationship between two variables, from their ranks rather than their raw values. For identical ranks on both variables, the coefficient is exactly 1 (perfect monotonic correlation); for exactly reversed ranks, it is exactly −1.
Explanation
Unlike the Pearson correlation coefficient, which measures the strength of a strictly linear relationship between two variables from their raw values, the Spearman coefficient works on the ranks of each observation (1 for the smallest value, 2 for the next, and so on) rather than the values themselves. This difference lets it detect a monotonic relationship (one variable always increasing when the other increases, or always when the other decreases) even if that relationship is not perfectly linear — for example an increasing exponential or logarithmic relationship, which Pearson correlation would underestimate. The formula used here, ρ = 1 − (6 × Σd²) ÷ (n × (n² − 1)), where d is the gap between the ranks of each pair of observations, is a simplified version that assumes no ties (two observations sharing the same rank): with ties, a more general formula equivalent to the Pearson coefficient computed directly on the average ranks must be used instead. Like the Pearson coefficient, the Spearman one always ranges between −1 (perfect decreasing monotonic relationship) and +1 (perfect increasing monotonic relationship), a value close to 0 indicating no detectable monotonic relationship.
Example: X at ranks 1,2,3,4 paired with Y at ranks 2,1,4,3
Inputs
Rank pairs (X,Y): (1,2), (2,1), (3,4), (4,3).
Calculation
Rank gaps: d₁=1−2=−1, d₂=2−1=1, d₃=3−4=−1, d₄=4−3=1. Sum of squares: 1+1+1+1=4. ρ = 1 − (6×4) ÷ (4×(16−1)) = 1 − 24÷60 = 1 − 0.4 = 0.6.
Result
The Spearman correlation coefficient of these ranks is 0.6, a moderate positive monotonic relationship.
Frequently asked questions
What is the difference between Spearman correlation and Pearson correlation?
Pearson correlation measures a strictly linear relationship from the raw values of the two variables, while Spearman measures a monotonic relationship (one that always goes in the same direction, without necessarily being a straight line) from their ranks. Two variables perfectly linked by a curved but always increasing relationship can have a Spearman coefficient of 1 while having a Pearson coefficient below 1.
What should you do if your data contains identical values (ties)?
The simplified formula used by this calculator assumes each rank is unique, with no two observations sharing the same rank. With ties, the standard practice is to assign these observations the average rank they would have occupied (for example, two values tied for ranks 2 and 3 both receive rank 2.5), then recompute the Pearson correlation directly on these ranks — a more general method, not covered by this calculator's simplified formula.
How do you interpret the coefficient value obtained?
As with Pearson correlation, a value close to +1 indicates a strong increasing monotonic relationship, a value close to −1 a strong decreasing monotonic relationship, and a value close to 0 no detectable monotonic relationship between the two variables. Unlike our simple linear regression calculator, which fits a precise line to the data, the Spearman coefficient only gives a measure of the strength and direction of the relationship, without specifying its equation.