Confidence Level Critical Value Calculator

This calculator finds the critical z value that matches any confidence level you choose, the exact multiplier used to build a confidence interval or run a z test in statistics. A 95 percent confidence level always corresponds to a two-tailed critical z of 1.96, but working out the right value for other levels, such as 90 percent or 99 percent, or knowing whether to use a one-tailed or two-tailed figure, is not something most people can do from memory or a printed table alone. Enter your chosen confidence level as a percentage and the calculator returns three figures: the two-tailed critical z, the main result used for most confidence intervals and non-directional tests, the one-tailed critical z used for directional, one-sided tests, and alpha, the significance level, which is simply 1 minus the confidence level expressed as a decimal. It works by feeding the confidence level through an accurate inverse standard normal, or probit, function, so the values match published statistical tables exactly. For example, entering 95 gives an alpha of 0.05, a two-tailed z of 1.96 and a one-tailed z of about 1.645. Use this tool for coursework, research reports or hypothesis testing whenever you need a reliable critical value without working through normal distribution tables by hand. Results are exact for any valid entry between 0 and 100 and are rounded for display.

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Confidence level (%)

One-tailed critical z

Alpha (significance)

The formula

For a confidence level with significance alpha = 1 minus the level, the two-tailed critical z is the inverse standard normal at 1 minus alpha/2, and the one-tailed critical z is the inverse standard normal at the confidence level. The calculator uses an accurate inverse normal (probit) function.

Worked example

A 95 percent confidence level has alpha = 0.05, so the two-tailed critical z is the inverse normal at 0.975, which is 1.96. The one-tailed value (at 0.95) is about 1.645. Enter 95 to confirm.

Frequently asked questions

What is the critical z for 95 percent?

1.96 for a two-tailed interval, and about 1.645 one-tailed.

What is alpha?

The significance level, equal to 1 minus the confidence level. For 95 percent confidence, alpha is 0.05.

Two-tailed or one-tailed?

Use two-tailed for a confidence interval or a non-directional test, one-tailed for a directional test.

Who this calculator is for

This calculator is for statistics students, researchers and analysts.

What this calculator assumes

You enter valid numbers.
The standard formula is applied.
Results are rounded for display.

Formula and sources

Related calculators

Standard Deviation Calculator: spread of data.
Z-Score Calculator: standard score.
Mean Median Mode Calculator: averages.

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