The standard z critical value for the most commonly used confidence levels, for both one-tailed and two-tailed tests.
How it works
These are well-established, widely tabulated constants for the standard normal distribution — not computed on the fly, but looked up directly for the chosen confidence level and test type.
What this does not include
This does not include t-distribution critical values, which additionally depend on degrees of freedom and require a much larger table — this calculator covers the z (normal distribution) critical values only.
How to use this calculator
- Select the confidence level and test type.
A worked example
95% confidence, two-tailed test: critical z-value = 1.96 — the most commonly cited critical value in introductory statistics.
95% confidence, one-tailed test: critical z-value = 1.645 — smaller than the two-tailed value, since all the tail probability sits on one side instead of splitting between two.
99% confidence, two-tailed: 2.576.
What the variables mean
| Variable | Meaning |
|---|---|
| Confidence level | How confident the interval or test should be |
| Tails | Whether the test checks for a difference in one direction only, or either direction |
Edge cases worth knowing
A one-tailed test has a smaller critical value than a two-tailed test at the same confidence level — all the rejection region concentrates on one side rather than splitting between both tails.
A higher confidence level always means a larger critical value — requiring more certainty pushes the threshold further out into the distribution’s tail.
Frequently asked questions
Why is 1.96 such a commonly cited critical value?
It’s the two-tailed z critical value for the widely used 95% confidence level, making it one of the most frequently referenced numbers in introductory statistics.
When should I use a one-tailed vs. two-tailed critical value?
A one-tailed test is used when only testing for an effect in one specific direction; a two-tailed test (more common) accounts for an effect in either direction.
Why isn’t the t-distribution included here?
T-distribution critical values additionally depend on degrees of freedom, requiring a much larger table than the fixed z-distribution values this calculator covers.
