F Critical Value Calculator
Calculate critical values for the F-distribution to determine statistical significance in ANOVA and regression analysis
Degrees of Freedom
Significance Level (α)
F Distribution Results
Enter your parameters to calculate the F critical value for your hypothesis test.
F Distribution Visualization
📊 Common F Critical Values
| df₁\df₂ | 1 | 2 | 3 | 4 | 5 | 10 | 20 | 30 | 50 | 100 | ∞ |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 161.45 | 199.50 | 215.71 | 224.58 | 230.16 | 241.88 | 248.01 | 250.10 | 251.77 | 253.04 | 254.31 |
| 2 | 18.51 | 19.00 | 19.16 | 19.25 | 19.30 | 19.40 | 19.45 | 19.46 | 19.48 | 19.49 | 19.50 |
| 3 | 10.13 | 9.55 | 9.28 | 9.12 | 9.01 | 8.79 | 8.66 | 8.62 | 8.58 | 8.55 | 8.53 |
| 4 | 7.71 | 6.94 | 6.59 | 6.39 | 6.26 | 5.96 | 5.80 | 5.75 | 5.70 | 5.66 | 5.63 |
| 5 | 6.61 | 5.79 | 5.41 | 5.19 | 5.05 | 4.74 | 4.56 | 4.50 | 4.44 | 4.41 | 4.37 |
| 10 | 4.96 | 4.10 | 3.71 | 3.48 | 3.33 | 2.98 | 2.77 | 2.70 | 2.64 | 2.59 | 2.54 |
| 20 | 4.35 | 3.49 | 3.10 | 2.87 | 2.71 | 2.35 | 2.12 | 2.04 | 1.97 | 1.91 | 1.84 |
| 30 | 4.17 | 3.32 | 2.92 | 2.69 | 2.53 | 2.16 | 1.93 | 1.84 | 1.76 | 1.70 | 1.62 |
Note: Values shown are for α = 0.05 (5% significance level)
| df₁\df₂ | 1 | 2 | 3 | 4 | 5 | 10 | 20 | 30 | 50 | 100 | ∞ |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 4052.18 | 4999.50 | 5403.35 | 5624.58 | 5763.65 | 6055.85 | 6208.73 | 6256.26 | 6294.57 | 6333.84 | 6365.86 |
| 2 | 98.50 | 99.00 | 99.17 | 99.25 | 99.30 | 99.40 | 99.45 | 99.47 | 99.48 | 99.49 | 99.50 |
| 3 | 34.12 | 30.82 | 29.46 | 28.71 | 28.24 | 26.92 | 25.99 | 25.69 | 25.41 | 25.19 | 24.96 |
| 4 | 21.20 | 18.00 | 16.69 | 15.98 | 15.52 | 14.17 | 13.17 | 12.84 | 12.53 | 12.28 | 12.02 |
| 5 | 16.26 | 13.27 | 12.06 | 11.39 | 10.97 | 9.68 | 8.71 | 8.38 | 8.08 | 7.82 | 7.56 |
| 10 | 10.04 | 7.56 | 6.55 | 5.99 | 5.64 | 4.71 | 3.86 | 3.56 | 3.28 | 3.03 | 2.76 |
| 20 | 8.10 | 5.85 | 4.94 | 4.43 | 4.10 | 3.23 | 2.46 | 2.16 | 1.88 | 1.63 | 1.32 |
| 30 | 7.56 | 5.39 | 4.51 | 4.02 | 3.70 | 2.88 | 2.14 | 1.84 | 1.57 | 1.32 | 0.99 |
Note: Values shown are for α = 0.01 (1% significance level)
| df₁\df₂ | 1 | 2 | 3 | 4 | 5 | 10 | 20 | 30 | 50 | 100 | ∞ |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 405284 | 499999.5 | 540379 | 562500 | 576405 | 605621 | 620907 | 625764 | 629626 | 633145 | 636619 |
| 2 | 998.50 | 999.00 | 999.17 | 999.25 | 999.30 | 999.40 | 999.45 | 999.47 | 999.48 | 999.49 | 999.50 |
| 3 | 167.03 | 148.50 | 141.11 | 137.10 | 134.58 | 127.35 | 122.40 | 120.68 | 119.08 | 117.73 | 116.31 |
| 4 | 74.14 | 61.25 | 56.18 | 53.44 | 51.71 | 46.99 | 43.69 | 42.47 | 41.37 | 40.48 | 39.52 |
| 5 | 47.18 | 37.12 | 33.20 | 31.09 | 29.75 | 26.07 | 23.20 | 22.24 | 21.34 | 20.58 | 19.76 |
| 10 | 21.04 | 14.91 | 12.55 | 11.28 | 10.48 | 8.59 | 6.99 | 6.35 | 5.77 | 5.20 | 4.56 |
| 20 | 14.02 | 9.44 | 7.64 | 6.70 | 6.10 | 4.71 | 3.56 | 3.10 | 2.70 | 2.30 | 1.83 |
| 30 | 12.22 | 8.02 | 6.35 | 5.51 | 4.98 | 3.73 | 2.70 | 2.31 | 1.96 | 1.62 | 1.18 |
Note: Values shown are for α = 0.001 (0.1% significance level)
📚 Understanding F Critical Values
What is an F Critical Value?
The F critical value is the threshold value that your calculated F-statistic must exceed to reject the null hypothesis in ANOVA or regression analysis. It's determined by your chosen significance level (α) and the degrees of freedom for your numerator and denominator.
When to Use It
F critical values are used in analysis of variance (ANOVA), regression analysis, and other statistical tests comparing variances. They help determine if group means are significantly different or if a regression model explains a significant portion of variance.
How to Interpret
If your calculated F-statistic > F critical value, reject the null hypothesis (significant result). If F-statistic ≤ F critical value, fail to reject the null (not significant). The smaller the α, the larger the critical value needed for significance.
Degrees of Freedom
df₁ (numerator) typically represents the number of groups minus 1 in ANOVA. df₂ (denominator) represents the total number of observations minus the number of groups. In regression, df₁ is the number of predictors, df₂ is n - predictors - 1.
F Distribution Shape
The F distribution is right-skewed and its shape changes with the degrees of freedom. As df₁ and df₂ increase, the distribution becomes more symmetric and approaches a normal distribution.
Common Mistakes
1) Using the wrong degrees of freedom. 2) Misinterpreting the direction of the test (F-tests are always right-tailed). 3) Choosing inappropriate significance levels without justification. 4) Ignoring assumptions like normality and homogeneity of variance.
Note: This calculator provides critical values for the F-distribution based on standard statistical tables. For extremely large degrees of freedom or unusual significance levels, more precise calculations may be needed. Always verify critical values with statistical software when conducting formal hypothesis tests.