# Critical Value Calculator

Free critical value calculator for z, t, chi-square, and F distributions. Get critical values for any significance level and degrees of freedom.

## What this calculates

Look up critical values for the most common statistical distributions: z (standard normal), Student's t, chi-square, and F. Enter your significance level and degrees of freedom to find the threshold for hypothesis testing.

## Inputs

- **Distribution** — options: Z (Standard Normal), t (Student's t), Chi-Square (chi^2), F (Fisher) — Select which distribution to find the critical value for.
- **Significance Level (alpha)** — min 0.001, max 0.5 — Significance level (typically 0.05, 0.01, or 0.10).
- **Degrees of Freedom (df1)** — min 1, max 1000 — Degrees of freedom (for t, chi-square) or numerator df (for F).
- **Degrees of Freedom 2 (df2, F only)** — min 1, max 1000 — Denominator degrees of freedom (only for F distribution).
- **Tail Type** — options: One-Tailed, Two-Tailed — One-tailed tests use alpha directly; two-tailed uses alpha/2.

## Outputs

- **Critical Value** — The critical value for the chosen distribution and parameters.
- **Rejection Region p-value** — The area in the tail(s) beyond the critical value.
- **Rejection Region** — formatted as text — Description of when to reject the null hypothesis.

## Details

Critical values are the boundary points that define rejection regions in hypothesis testing. If your test statistic exceeds the critical value, you reject the null hypothesis at the chosen significance level.

Z critical values are used for large-sample tests and proportions. Common values: 1.645 (alpha=0.05, one-tailed), 1.960 (alpha=0.05, two-tailed), 2.576 (alpha=0.01, two-tailed). T critical values are used for small-sample means and depend on degrees of freedom; they approach z values as df increases. Chi-square critical values are used for goodness-of-fit and independence tests. F critical values are used for ANOVA and comparing variances.

One-tailed vs two-tailed: One-tailed tests use the full significance level in one direction. Two-tailed tests split alpha equally between both tails. Use two-tailed when you want to detect differences in either direction.

## Frequently Asked Questions

**Q: What is the z critical value for 95% confidence?**

A: For a 95% confidence level (alpha = 0.05, two-tailed), the z critical value is 1.96. This means the rejection region is z < -1.96 or z > 1.96. For a one-tailed test at 95%, the critical value is 1.645.

**Q: How do degrees of freedom affect the t critical value?**

A: With fewer degrees of freedom, the t distribution has heavier tails, so critical values are larger (making it harder to reject H0). As df increases, the t distribution approaches the standard normal, and t critical values approach z critical values. By df = 30, they are very close.

**Q: When do I use a one-tailed vs two-tailed test?**

A: Use a one-tailed test when you have a directional hypothesis (e.g., treatment is better, not just different). Use a two-tailed test when you want to detect any difference, regardless of direction. Two-tailed tests are more conservative and more commonly used.

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Source: https://vastcalc.com/calculators/statistics/critical-value
Category: Statistics
Last updated: 2026-04-21