One Dimensional Wasserstein Distance Calculator
Calculate exact empirical first-Wasserstein distance between two equally weighted numeric samples, even with unequal lengths.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Sort distinct combined sample knots and integrate the absolute empirical CDF gap over each interval.
W1=∫|FA(x)−FB(x)| dx
Worked example
Samples (0,1) and (1,2) have empirical first-Wasserstein distance 1, in the same unit as the input values.
Assumptions and input details
Each observation has equal within-sample weight. This is a one-dimensional empirical transport distance, not a multivariate distance, standardized effect or p-value. Units and coordinate scale must match.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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