Pearson Correlation Critical Values Table (r)

The critical values of the Pearson correlation coefficient (r) tell you how large a correlation must be, for a given sample size, to be statistically significant. Find the row for your degrees of freedom (df = n − 2, where n is the number of paired observations) and the column for your two-tailed significance level α. If your observed |r| is greater than or equal to the table value, the correlation is significant at that level.

How to read the table

Columns are two-tailed α levels. For a one-tailed test, the same value corresponds to half the α (e.g. the α = 0.05 two-tailed column is the α = 0.025 one-tailed critical value).

Example: You collect n = 12 paired observations, so df = 10. The two-tailed critical value at α = 0.05 is 0.5760. If your computed correlation is r = 0.64, then 0.64 > 0.576, so the correlation is statistically significant (p < 0.05).

df (n−2)	α=0.10	α=0.05	α=0.02	α=0.01
1	0.9877	0.9969	0.9995	0.9999
2	0.9000	0.9500	0.9800	0.9900
3	0.8054	0.8783	0.9343	0.9587
4	0.7293	0.8114	0.8822	0.9172
5	0.6694	0.7545	0.8329	0.8745
6	0.6215	0.7067	0.7887	0.8343
7	0.5822	0.6664	0.7498	0.7977
8	0.5494	0.6319	0.7155	0.7646
9	0.5214	0.6021	0.6851	0.7348
10	0.4973	0.5760	0.6581	0.7079
11	0.4762	0.5529	0.6339	0.6835
12	0.4575	0.5324	0.6120	0.6614
13	0.4409	0.5140	0.5923	0.6411
14	0.4259	0.4973	0.5742	0.6226
15	0.4124	0.4821	0.5577	0.6055
16	0.4000	0.4683	0.5425	0.5897
17	0.3887	0.4555	0.5285	0.5751
18	0.3783	0.4438	0.5155	0.5614
19	0.3687	0.4329	0.5034	0.5487
20	0.3598	0.4227	0.4921	0.5368
25	0.3233	0.3809	0.4451	0.4869
30	0.2960	0.3494	0.4093	0.4487
35	0.2746	0.3246	0.3810	0.4182
40	0.2573	0.3044	0.3578	0.3932
45	0.2429	0.2876	0.3384	0.3721
50	0.2306	0.2732	0.3218	0.3542
60	0.2108	0.2500	0.2948	0.3248
70	0.1954	0.2319	0.2737	0.3017
80	0.1829	0.2172	0.2565	0.2830
90	0.1726	0.2050	0.2422	0.2673
100	0.1638	0.1946	0.2301	0.2540

Computed with SciPy: r_crit = t_crit / √(df + t_crit²), where t_crit = t.ppf(1−α/2, df). Values match standard published correlation tables. See the methodology page.

When you need this

Use it to check significance of a Pearson correlation by hand, or to sanity-check software output. Remember that significance is not the same as importance — a small but significant r can explain very little variance. Run the full test, including the exact p-value and r², with the correlation calculator, and read correlation vs causation before drawing conclusions.

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Pearson Correlation Critical Values (r)

How to read the table

When you need this

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