Mann–Whitney U Calculator
Estimate a rank-based comparison between two independent samples when you know their sizes and the rank sum for the first sample. The tool shows the method and key assumptions so you can inspect how the input values lead to the estimate.
How to use this calculator
- Enter sample 1 size using the unit and definition shown beside the input.
- Enter sample 2 size using the unit and definition shown beside the input.
- Enter sum of ranks for sample 1 using the unit and definition shown beside the input.
- Check that all values refer to the same time period and scenario.
- Review the outputs alongside the assumptions before using them in a decision.
Formula and assumptions
U₁=R₁−n₁(n₁+1)/2; μU=n₁n₂/2; approximate variance=n₁n₂(n₁+n₂+1)/12.
- This normal approximation omits tie correction and is intended as a transparent estimate for sufficiently large samples. Use a statistical package for exact inference, tied ranks, or formal research reporting.
- The estimate is calculated from values you enter. It does not connect to external accounts, obtain live prices, or validate local regulations or engineering specifications.
Worked examples
Worked example
For n₁=18, n₂=20 and rank sum R₁=390, U₁=219 before the continuity-adjusted normal approximation.
Enter both sample sizes and the rank sum calculated from the combined ranking.
Check ties, independence and sample-size assumptions before reporting a p-value.
Understanding the result
This normal approximation omits tie correction and is intended as a transparent estimate for sufficiently large samples. Use a statistical package for exact inference, tied ranks, or formal research reporting.
Change one input at a time to see how sensitive the output is to that assumption.
Important notes
This normal approximation omits tie correction and is intended as a transparent estimate for sufficiently large samples. Use a statistical package for exact inference, tied ranks, or formal research reporting.
Frequently asked questions
What formula does the Mann–Whitney U Calculator use?
U₁=R₁−n₁(n₁+1)/2; μU=n₁n₂/2; approximate variance=n₁n₂(n₁+n₂+1)/12.
What should I verify before relying on the result?
This normal approximation omits tie correction and is intended as a transparent estimate for sufficiently large samples. Use a statistical package for exact inference, tied ranks, or formal research reporting.
Can I compare different scenarios?
Yes. Change one assumption at a time, keep units and definitions consistent, and save the inputs used for each comparison.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate Standard Deviation — Learn what standard deviation measures, the population and sample formulas, and how to interpret the result.
- How to Calculate a Z-Score — Learn how a z-score shows how far a value is from the mean in standard-deviation units.
- Standard Deviation — Understand standard deviation as a measure of spread and the difference between population and sample standard deviation.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.