Mann–Whitney U Critical Values Table (α=0.05)

The Mann–Whitney U critical values table gives the largest U for which two independent samples differ significantly at α = 0.05 (two-tailed). Compute U for both groups, take the smaller value, and compare it to the table entry for your sample sizes n₁ and n₂. Reject the null hypothesis if your U is less than or equal to the table value. A dash (—) means no significant result is possible at this α for samples that small.

How to read it

These are exact critical values from the Mann–Whitney null distribution (not the normal approximation), which matters because the test is most often used with small samples. The relationship note: U₁ + U₂ = n₁n₂, so you only need the smaller U.

Example: n₁ = n₂ = 8. The critical value is 13. If the smaller computed U is 11, then 11 ≤ 13, so the two groups differ significantly (p < 0.05). If U were 15, you would fail to reject.

n₁ \ n₂	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
3	—	—	0	1	1	2	2	3	3	4	4	5	5	6	6	7	7	8
4	—	0	1	2	3	4	4	5	6	7	8	9	10	11	11	12	13	14
5	0	1	2	3	5	6	7	8	9	11	12	13	14	15	17	18	19	20
6	1	2	3	5	6	8	10	11	13	14	16	17	19	21	22	24	25	27
7	1	3	5	6	8	10	12	14	16	18	20	22	24	26	28	30	32	34
8	2	4	6	8	10	13	15	17	19	22	24	26	29	31	34	36	38	41
9	2	4	7	10	12	15	17	20	23	26	28	31	34	37	39	42	45	48
10	3	5	8	11	14	17	20	23	26	29	33	36	39	42	45	48	52	55
11	3	6	9	13	16	19	23	26	30	33	37	40	44	47	51	55	58	62
12	4	7	11	14	18	22	26	29	33	37	41	45	49	53	57	61	65	69
13	4	8	12	16	20	24	28	33	37	41	45	50	54	59	63	67	72	76
14	5	9	13	17	22	26	31	36	40	45	50	55	59	64	69	74	78	83
15	5	10	14	19	24	29	34	39	44	49	54	59	64	70	75	80	85	90
16	6	11	15	21	26	31	37	42	47	53	59	64	70	75	81	86	92	98
17	6	11	17	22	28	34	39	45	51	57	63	69	75	81	87	93	99	105
18	7	12	18	24	30	36	42	48	55	61	67	74	80	86	93	99	106	112
19	7	13	19	25	32	38	45	52	58	65	72	78	85	92	99	106	113	119
20	8	14	20	27	34	41	48	55	62	69	76	83	90	98	105	112	119	127

Exact values computed from the Mann–Whitney U distribution and verified against standard published tables. For larger samples use the normal approximation (z), which the calculator applies automatically. See the methodology page.

When to use the Mann–Whitney U test

It is the non-parametric alternative to the independent two-sample t-test, used when data is ordinal or badly non-normal. Run it directly — with the exact p-value — in the Mann–Whitney U calculator. For paired data, use the Wilcoxon signed-rank test instead.

All tables Mann–Whitney Calculator T-Test Which test?

Mann–Whitney U Critical Values (α = 0.05, two-tailed)

How to read it

When to use the Mann–Whitney U test

Related

n₁ \ n₂	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
3	—	—	0	1	1	2	2	3	3	4	4	5	5	6	6	7	7	8
4	—	0	1	2	3	4	4	5	6	7	8	9	10	11	11	12	13	14
5	0	1	2	3	5	6	7	8	9	11	12	13	14	15	17	18	19	20
6	1	2	3	5	6	8	10	11	13	14	16	17	19	21	22	24	25	27
7	1	3	5	6	8	10	12	14	16	18	20	22	24	26	28	30	32	34
8	2	4	6	8	10	13	15	17	19	22	24	26	29	31	34	36	38	41
9	2	4	7	10	12	15	17	20	23	26	28	31	34	37	39	42	45	48
10	3	5	8	11	14	17	20	23	26	29	33	36	39	42	45	48	52	55
11	3	6	9	13	16	19	23	26	30	33	37	40	44	47	51	55	58	62
12	4	7	11	14	18	22	26	29	33	37	41	45	49	53	57	61	65	69
13	4	8	12	16	20	24	28	33	37	41	45	50	54	59	63	67	72	76
14	5	9	13	17	22	26	31	36	40	45	50	55	59	64	69	74	78	83
15	5	10	14	19	24	29	34	39	44	49	54	59	64	70	75	80	85	90
16	6	11	15	21	26	31	37	42	47	53	59	64	70	75	81	86	92	98
17	6	11	17	22	28	34	39	45	51	57	63	69	75	81	87	93	99	105
18	7	12	18	24	30	36	42	48	55	61	67	74	80	86	93	99	106	112
19	7	13	19	25	32	38	45	52	58	65	72	78	85	92	99	106	113	119
20	8	14	20	27	34	41	48	55	62	69	76	83	90	98	105	112	119	127

n₁ \ n₂	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
3	—	—	0	1	1	2	2	3	3	4	4	5	5	6	6	7	7	8
4	—	0	1	2	3	4	4	5	6	7	8	9	10	11	11	12	13	14
5	0	1	2	3	5	6	7	8	9	11	12	13	14	15	17	18	19	20
6	1	2	3	5	6	8	10	11	13	14	16	17	19	21	22	24	25	27
7	1	3	5	6	8	10	12	14	16	18	20	22	24	26	28	30	32	34
8	2	4	6	8	10	13	15	17	19	22	24	26	29	31	34	36	38	41
9	2	4	7	10	12	15	17	20	23	26	28	31	34	37	39	42	45	48
10	3	5	8	11	14	17	20	23	26	29	33	36	39	42	45	48	52	55
11	3	6	9	13	16	19	23	26	30	33	37	40	44	47	51	55	58	62
12	4	7	11	14	18	22	26	29	33	37	41	45	49	53	57	61	65	69
13	4	8	12	16	20	24	28	33	37	41	45	50	54	59	63	67	72	76
14	5	9	13	17	22	26	31	36	40	45	50	55	59	64	69	74	78	83
15	5	10	14	19	24	29	34	39	44	49	54	59	64	70	75	80	85	90
16	6	11	15	21	26	31	37	42	47	53	59	64	70	75	81	86	92	98
17	6	11	17	22	28	34	39	45	51	57	63	69	75	81	87	93	99	105
18	7	12	18	24	30	36	42	48	55	61	67	74	80	86	93	99	106	112
19	7	13	19	25	32	38	45	52	58	65	72	78	85	92	99	106	113	119
20	8	14	20	27	34	41	48	55	62	69	76	83	90	98	105	112	119	127

n₁ \ n₂	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
3	—	—	0	1	1	2	2	3	3	4	4	5	5	6	6	7	7	8
4	—	0	1	2	3	4	4	5	6	7	8	9	10	11	11	12	13	14
5	0	1	2	3	5	6	7	8	9	11	12	13	14	15	17	18	19	20
6	1	2	3	5	6	8	10	11	13	14	16	17	19	21	22	24	25	27
7	1	3	5	6	8	10	12	14	16	18	20	22	24	26	28	30	32	34
8	2	4	6	8	10	13	15	17	19	22	24	26	29	31	34	36	38	41
9	2	4	7	10	12	15	17	20	23	26	28	31	34	37	39	42	45	48
10	3	5	8	11	14	17	20	23	26	29	33	36	39	42	45	48	52	55
11	3	6	9	13	16	19	23	26	30	33	37	40	44	47	51	55	58	62
12	4	7	11	14	18	22	26	29	33	37	41	45	49	53	57	61	65	69
13	4	8	12	16	20	24	28	33	37	41	45	50	54	59	63	67	72	76
14	5	9	13	17	22	26	31	36	40	45	50	55	59	64	69	74	78	83
15	5	10	14	19	24	29	34	39	44	49	54	59	64	70	75	80	85	90
16	6	11	15	21	26	31	37	42	47	53	59	64	70	75	81	86	92	98
17	6	11	17	22	28	34	39	45	51	57	63	69	75	81	87	93	99	105
18	7	12	18	24	30	36	42	48	55	61	67	74	80	86	93	99	106	112
19	7	13	19	25	32	38	45	52	58	65	72	78	85	92	99	106	113	119
20	8	14	20	27	34	41	48	55	62	69	76	83	90	98	105	112	119	127