Critical Value Calculator
Find critical values for one and two-tailed tests at a chosen significance level.
About Critical Value Calculator
A two-tailed test splits the significance level between both tails, so its critical value is larger than a one-tailed test at the same alpha. At 5 per cent these are 1.96 and 1.645 respectively. Choosing one-tailed after seeing the data inflates the false positive rate, which is why the direction must be specified in advance.
Formula
Critical Value
The critical value is the z with tail area α (one-tailed) or α/2 (two-tailed)
- rejection region
- Values of the statistic that lead to rejecting the null hypothesis
Worked example
With the default values below, Critical Value Calculator returns Critical Value of 1.96039. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Significance levelaccepts 0.01–50 %
- 5 %
- Test typeone of One-tailed, Two-tailed
- Two-tailed
- Your test statistic
- 2.1
Results
- Critical Value
- 1.96039
- Decision
- Reject H0 — the statistic falls in the rejection region
- Area in Each Tail
- 0.025000
- Amount the Statistic Exceeds the Critical Value
- 0.13961
- Equivalent Confidence Level
- 95.000%
Step by step
- 1Values used
- 2Critical Value
- 3Critical Value= 1.96039
- 4Decision= Reject H0 — the statistic falls in the rejection region
- 5Area in Each Tail= 0.025000
- 6Amount the Statistic Exceeds the Critical Value= 0.13961
- 7Equivalent Confidence Level= 95.000
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How is Critical Value calculated?
The critical value is the z with tail area α (one-tailed) or α/2 (two-tailed) A two-tailed test splits the significance level between both tails, so its critical value is larger than a one-tailed test at the same alpha. At 5 per cent these are 1.96 and 1.645 respectively.
Why does Critical Value matter?
Choosing one-tailed after seeing the data inflates the false positive rate, which is why the direction must be specified in advance.
What values do I need to enter?
This calculator takes 3 inputs: Significance level, Test type, Your test statistic. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.