How does the F-Distribution Calculator work?

F = (s₁²/σ₁²) / (s₂²/σ₂²) Then: Degrees of freedom: df₁ (numerator) and df₂ (denominator) Then: If F > critical value: reject H₀ at chosen α Then: F-test used in ANOVA, regression significance.

Can you give an example of how to use the F-Distribution Calculator?

Example: Input F=3.5, df₁=3, df₂=20, α=0.05 gives a result of Critical value ≈ 3.10; F > critical, reject H₀.

Is the F-Distribution Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the F-Distribution Calculator?

Our F-Distribution Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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F-Distribution Calculator

df₁ (numerator)

df₂ (denominator)

F statistic

✓F-Distribution Result

Critical Value α=0.05 (approx)

3.33

F=3.33 ≤ 3.33 → Fail to reject H₀

The F-distribution arises in statistical tests that compare variances or mean squares, such as ANOVA and regression analysis. The F-statistic is the ratio of two chi-squared distributions divided by their degrees of freedom.

Symbol	Name	Unit	Description
s₁²	variance of first sample	—	—
s₂²	variance of second sample	—	—
F	F-statistic	—	ratio of variances
df₁, df₂	degrees of freedom	—	for numerator and denominator

df₁/df₂	5	10	20	∞
1	6.61	4.96	4.35	3.84
3	5.41	3.71	3.10	2.60
5	4.39	3.33	2.71	2.21
10	3.33	2.98	2.35	1.83

References

›F-distribution — Wikipedia

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F critical value and p-value for ANOVA tests. Instant result with formula, examples and step-by-step calculation. Free online calculator.

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F-Distribution Calculator