Critical Value Calculator
Calculate accurate critical values for Z, T, chi-square, and F distributions. Enter your alpha level, tail type, and degrees of freedom to quickly find the cutoff value used in confidence intervals, hypothesis tests, ANOVA, regression, and statistical decision making.
Enter Test Details
Result
Your critical value will appear here
Choose the distribution, alpha level, and tail type, then click calculate.
What Is a Critical Value?
A critical value is a cutoff point used in statistics to decide whether a test result falls inside or outside the rejection region. It helps you compare your test statistic with a known boundary from a probability distribution.
Used when sample size is large or population standard deviation is known.
Used for smaller samples when population standard deviation is unknown.
Used in variance tests, goodness-of-fit tests, and independence tests.
Used in ANOVA, regression testing, and comparing two variances.
How It Works
- Select the distribution type: Z, T, chi-square, or F.
- Choose whether your test is left-tailed, right-tailed, or two-tailed.
- Enter the alpha value, such as 0.05 for a 95% confidence level.
- Add degrees of freedom when required by the selected distribution.
- Click calculate to get the critical value and decision boundary.
This critical value calculator is useful for students, researchers, data analysts, finance professionals, and anyone working with statistical testing.
Frequently Asked Questions
What is the critical value for 95% confidence?
For a two-tailed Z test with 95% confidence, the critical values are approximately -1.96 and +1.96. For T, chi-square, and F distributions, the value depends on degrees of freedom.
What alpha should I use?
The most common alpha value is 0.05, which represents a 5% significance level. Some studies use 0.01 for stricter testing or 0.10 for more flexible testing.
What is the difference between one-tailed and two-tailed critical values?
A one-tailed test checks one direction only, while a two-tailed test checks both directions. In a two-tailed test, alpha is divided between the left and right tails.
When should I use a T critical value?
Use a T critical value when your sample size is small or when the population standard deviation is unknown. The T distribution also requires degrees of freedom.
Can this calculator be used for ANOVA?
Yes. For ANOVA, select the F critical value option and enter numerator and denominator degrees of freedom based on your ANOVA table.