Critical Value Calculator
Use this tool to compute Z or T critical values for hypothesis tests and confidence intervals.
What is a critical value?
A critical value is the cutoff point that separates your rejection region from your non-rejection region in hypothesis testing. In plain terms, it tells you how extreme a test statistic must be before you consider the result statistically significant.
If you've searched for an omni calculator critical value style tool, you're usually trying to quickly find:
- Z critical values (like 1.645, 1.96, or 2.576),
- T critical values based on degrees of freedom,
- one-tailed or two-tailed thresholds for a chosen confidence level.
How this calculator works
1) Choose a distribution
Pick Z if you're working with the standard normal setup. Pick T when your sample is smaller and population standard deviation is unknown.
2) Enter confidence level
Confidence level determines significance level:
Example: 95% confidence means α = 0.05.
3) Select tail type
- Two-tailed: split α across both tails.
- Right-tailed: put α in the right tail.
- Left-tailed: put α in the left tail.
4) For t-distribution, provide degrees of freedom
Degrees of freedom are often n − 1 for a one-sample t procedure.
Quick interpretation guide
Suppose your two-tailed critical values are ±1.96. If your test statistic is greater than 1.96 or less than -1.96, your result falls in the rejection region at the chosen significance level.
For a right-tailed setup with a critical value of 1.645, reject only if your test statistic exceeds 1.645.
Common critical values people memorize
- 90% confidence (two-tailed z): ±1.645
- 95% confidence (two-tailed z): ±1.96
- 99% confidence (two-tailed z): ±2.576
T critical values vary with degrees of freedom, which is why a calculator is so helpful.
Common mistakes to avoid
- Mixing up one-tailed and two-tailed tests.
- Using z-values when t-values are appropriate.
- Entering confidence level as a decimal when percentage is expected.
- Forgetting that lower-tail critical values are negative in symmetric distributions.
FAQ
Is this the same as p-value?
No. The critical value is a threshold. The p-value is the probability of seeing data as extreme as your sample under the null hypothesis.
Can I use this for confidence intervals?
Yes. Critical values are the multiplier in many interval formulas, such as estimate ± (critical value × standard error).
Why does t critical value get closer to z as df increases?
Because the t-distribution converges to the normal distribution as sample size (and df) grows.