Statistical Tables/Pearson Correlation Critical Values (r Table)

Regression & Correlation

Pearson Correlation Critical Values (r Table)

The smallest correlation coefficient that counts as statistically significant, for your sample size and significance level.

Critical values of |r|, df = n − 2

df	Two-tailed α (one-tailed α in grey)
df	0.1 (0.05)	0.05 (0.025)	0.02 (0.01)	0.01 (0.005)	0.001 (0.0005)
1	0.9877	0.9969	0.9995	0.9999	1.0000
2	0.9000	0.9500	0.9800	0.9900	0.9990
3	0.8054	0.8783	0.9343	0.9587	0.9911
4	0.7293	0.8114	0.8822	0.9172	0.9741
5	0.6694	0.7545	0.8329	0.8745	0.9509
6	0.6215	0.7067	0.7887	0.8343	0.9249
7	0.5822	0.6664	0.7498	0.7977	0.8983
8	0.5494	0.6319	0.7155	0.7646	0.8721
9	0.5214	0.6021	0.6851	0.7348	0.8470
10	0.4973	0.5760	0.6581	0.7079	0.8233
11	0.4762	0.5529	0.6339	0.6835	0.8010
12	0.4575	0.5324	0.6120	0.6614	0.7800
13	0.4409	0.5140	0.5923	0.6411	0.7604
14	0.4259	0.4973	0.5742	0.6226	0.7419
15	0.4124	0.4821	0.5577	0.6055	0.7247
16	0.4000	0.4683	0.5425	0.5897	0.7084
17	0.3887	0.4555	0.5285	0.5751	0.6932
18	0.3783	0.4438	0.5155	0.5614	0.6788
19	0.3687	0.4329	0.5034	0.5487	0.6652
20	0.3598	0.4227	0.4921	0.5368	0.6524
21	0.3515	0.4132	0.4815	0.5256	0.6402
22	0.3438	0.4044	0.4716	0.5151	0.6287
23	0.3365	0.3961	0.4622	0.5052	0.6178
24	0.3297	0.3882	0.4534	0.4958	0.6074
25	0.3233	0.3809	0.4451	0.4869	0.5974
26	0.3172	0.3739	0.4372	0.4785	0.5880
27	0.3115	0.3673	0.4297	0.4705	0.5790
28	0.3061	0.3610	0.4226	0.4629	0.5703
29	0.3009	0.3550	0.4158	0.4556	0.5620
30	0.2960	0.3494	0.4093	0.4487	0.5541
35	0.2746	0.3246	0.3810	0.4182	0.5189
40	0.2573	0.3044	0.3578	0.3932	0.4896
45	0.2429	0.2876	0.3384	0.3721	0.4647
50	0.2306	0.2732	0.3218	0.3542	0.4432
60	0.2108	0.2500	0.2948	0.3248	0.4079
70	0.1954	0.2319	0.2737	0.3017	0.3798
80	0.1829	0.2172	0.2565	0.2830	0.3568
90	0.1726	0.2050	0.2422	0.2673	0.3375
100	0.1638	0.1946	0.2301	0.2540	0.3211
120	0.1496	0.1779	0.2104	0.2324	0.2943
150	0.1339	0.1593	0.1886	0.2083	0.2643
200	0.1161	0.1381	0.1636	0.1809	0.2298
300	0.0948	0.1129	0.1338	0.1480	0.1884
500	0.0735	0.0875	0.1038	0.1149	0.1464
1000	0.0520	0.0619	0.0735	0.0813	0.1038

Degrees of freedom are n − 2, where n is the number of paired observations. Your correlation is statistically significant if its absolute value is greater than or equal to the tabled value. Every value is derived exactly from the Student t critical value via r = t / √(df + t²).

How to use this tool

Count your paired observations, n, and subtract 2 to get the degrees of freedom.
Pick the column for your significance level (two-tailed unless you predicted the direction in advance).
Read the critical value where your df row meets that column.
If the absolute value of your r is at least the tabled value, the correlation is statistically significant.

Formula Reference

Degrees of freedom

df = n − 2

Critical r from critical t

r_crit = t_crit / √(df + t_crit²)

Equivalent t statistic

t = r √(n − 2) / √(1 − r²)

ArticlePearson Correlation CalcCorrelation Calculator ToolScatter Plot & Correlation Visualizer TableStudent t-Table GlossaryGlossary: Pearson Correlation

Frequently Asked Questions

Why do small samples need such large correlations?+

With only a handful of points, a strong-looking pattern can easily appear by chance. With 5 pairs (df = 3) you need |r| of at least 0.878 to be significant at α = 0.05 two-tailed; with 102 pairs (df = 100) about 0.195 is enough.

Does a significant r mean a strong relationship?+

No. Significance only says the correlation is unlikely to be exactly zero in the population. With large samples even a weak correlation like 0.2 is significant, so always report and interpret the size of r itself as well.

Where do these values come from?+

Testing r against zero is equivalent to a t-test with n − 2 degrees of freedom, so each critical r is converted exactly from the matching critical t value using r = t / √(df + t²).

Can I use this table for Spearman's rank correlation?+

Only as a rough guide for larger samples. Spearman's coefficient has its own exact small-sample distribution, and for small n its critical values differ noticeably from the Pearson ones listed here.

df	Two-tailed α (one-tailed α in grey)
1	0.9877	0.9969	0.9995	0.9999	1.0000
2	0.9000	0.9500	0.9800	0.9900	0.9990
3	0.8054	0.8783	0.9343	0.9587	0.9911
4	0.7293	0.8114	0.8822	0.9172	0.9741
5	0.6694	0.7545	0.8329	0.8745	0.9509
6	0.6215	0.7067	0.7887	0.8343	0.9249
7	0.5822	0.6664	0.7498	0.7977	0.8983
8	0.5494	0.6319	0.7155	0.7646	0.8721
9	0.5214	0.6021	0.6851	0.7348	0.8470
10	0.4973	0.5760	0.6581	0.7079	0.8233
11	0.4762	0.5529	0.6339	0.6835	0.8010
12	0.4575	0.5324	0.6120	0.6614	0.7800
13	0.4409	0.5140	0.5923	0.6411	0.7604
14	0.4259	0.4973	0.5742	0.6226	0.7419
15	0.4124	0.4821	0.5577	0.6055	0.7247
16	0.4000	0.4683	0.5425	0.5897	0.7084
17	0.3887	0.4555	0.5285	0.5751	0.6932
18	0.3783	0.4438	0.5155	0.5614	0.6788
19	0.3687	0.4329	0.5034	0.5487	0.6652
20	0.3598	0.4227	0.4921	0.5368	0.6524
21	0.3515	0.4132	0.4815	0.5256	0.6402
22	0.3438	0.4044	0.4716	0.5151	0.6287
23	0.3365	0.3961	0.4622	0.5052	0.6178
24	0.3297	0.3882	0.4534	0.4958	0.6074
25	0.3233	0.3809	0.4451	0.4869	0.5974
26	0.3172	0.3739	0.4372	0.4785	0.5880
27	0.3115	0.3673	0.4297	0.4705	0.5790
28	0.3061	0.3610	0.4226	0.4629	0.5703
29	0.3009	0.3550	0.4158	0.4556	0.5620
30	0.2960	0.3494	0.4093	0.4487	0.5541
35	0.2746	0.3246	0.3810	0.4182	0.5189
40	0.2573	0.3044	0.3578	0.3932	0.4896
45	0.2429	0.2876	0.3384	0.3721	0.4647
50	0.2306	0.2732	0.3218	0.3542	0.4432
60	0.2108	0.2500	0.2948	0.3248	0.4079
70	0.1954	0.2319	0.2737	0.3017	0.3798
80	0.1829	0.2172	0.2565	0.2830	0.3568
90	0.1726	0.2050	0.2422	0.2673	0.3375
100	0.1638	0.1946	0.2301	0.2540	0.3211
120	0.1496	0.1779	0.2104	0.2324	0.2943
150	0.1339	0.1593	0.1886	0.2083	0.2643
200	0.1161	0.1381	0.1636	0.1809	0.2298
300	0.0948	0.1129	0.1338	0.1480	0.1884
500	0.0735	0.0875	0.1038	0.1149	0.1464
1000	0.0520	0.0619	0.0735	0.0813	0.1038

Two-tailed α (one-tailed α in grey)

0.1 (0.05)

0.05 (0.025)

0.02 (0.01)

0.01 (0.005)

0.001 (0.0005)

0.9877

0.9969

0.9995

0.9999

1.0000

0.9000

0.9500

0.9800

0.9900

0.9990

0.8054

0.8783

0.9343

0.9587

0.9911

0.7293

0.8114

0.8822

0.9172

0.9741

0.6694

0.7545

0.8329

0.8745

0.9509

0.6215

0.7067

0.7887

0.8343

0.9249

0.5822

0.6664

0.7498

0.7977

0.8983

0.5494

0.6319

0.7155

0.7646

0.8721

0.5214

0.6021

0.6851

0.7348

0.8470

0.4973

0.5760

0.6581

0.7079

0.8233

0.4762

0.5529

0.6339

0.6835

0.8010

0.4575

0.5324

0.6120

0.6614

0.7800

0.4409

0.5140

0.5923

0.6411

0.7604

0.4259

0.4973

0.5742

0.6226

0.7419

0.4124

0.4821

0.5577

0.6055

0.7247

0.4000

0.4683

0.5425

0.5897

0.7084

0.3887

0.4555

0.5285

0.5751

0.6932

0.3783

0.4438

0.5155

0.5614

0.6788

0.3687

0.4329

0.5034

0.5487

0.6652

0.3598

0.4227

0.4921

0.5368

0.6524

0.3515

0.4132

0.4815

0.5256

0.6402

0.3438

0.4044

0.4716

0.5151

0.6287

0.3365

0.3961

0.4622

0.5052

0.6178

0.3297

0.3882

0.4534

0.4958

0.6074

0.3233

0.3809

0.4451

0.4869

0.5974

0.3172

0.3739

0.4372

0.4785

0.5880

0.3115

0.3673

0.4297

0.4705

0.5790

0.3061

0.3610

0.4226

0.4629

0.5703

0.3009

0.3550

0.4158

0.4556

0.5620

0.2960

0.3494

0.4093

0.4487

0.5541

0.2746

0.3246

0.3810

0.4182

0.5189

0.2573

0.3044

0.3578

0.3932

0.4896

0.2429

0.2876

0.3384

0.3721

0.4647

0.2306

0.2732

0.3218

0.3542

0.4432

0.2108

0.2500

0.2948

0.3248

0.4079

0.1954

0.2319

0.2737

0.3017

0.3798

0.1829

0.2172

0.2565

0.2830

0.3568

0.1726

0.2050

0.2422

0.2673

0.3375

100

0.1638

0.1946

0.2301

0.2540

0.3211

120

0.1496

0.1779

0.2104

0.2324

0.2943

150

0.1339

0.1593

0.1886

0.2083

0.2643

200

0.1161

0.1381

0.1636

0.1809

0.2298

300

0.0948

0.1129

0.1338

0.1480

0.1884

500

0.0735

0.0875

0.1038

0.1149

0.1464

1000

0.0520

0.0619

0.0735

0.0813

0.1038

How to use this tool

Count your paired observations, n, and subtract 2 to get the degrees of freedom.

Pick the column for your significance level (two-tailed unless you predicted the direction in advance).

Read the critical value where your df row meets that column.

If the absolute value of your r is at least the tabled value, the correlation is statistically significant.