Z Critical Value Calculator

Use this Z Critical Value Calculator to find the critical Z value for a left-tailed, right-tailed, or two-tailed hypothesis test. You simply need to enter your significance level (α), and the calculator will return the correct z critical value with a clear step-by-step explanation.

This calculator is designed for statistical tests that use z critical values. However, if you need to find other critical values, such as t, F, chi-square, or r (in one place), use our Critical Value Calculator instead.

Already have the z test statistic and want to make a decision using the p-value approach? Use our Z to P-Value Calculator to convert your z score into a p-value.

How to Use the Z Critical Value Calculator

Want to quickly find z critical values for hypothesis tests and confidence intervals without using z tables? This calculator gives you instant results and a clear step-by-step explanation.

To use the calculator:

1. Enter the significance level (α) as a decimal
2. Click Calculate.

The calculator will instantly return the two-tailed, right-tailed, and left-tailed critical values for your test. It starts by highlighting the two-tailed critical values because they are commonly used in many hypothesis tests and confidence interval problems. It then presents the corresponding left-tailed and right-tailed critical values to help you make decisions about directional hypothesis test problems.

After the results, the calculator provides a step-by-step explanation showing how each critical value is obtained from the standard normal distribution and how to use the values when making decisions about your hypothesis.

Example 1. Two-Tailed Test

Find the z critical values for a two-tailed hypothesis test at a 1% significance level.

Solution

From the question, the significance level, α = 1%, which is equivalent to 0.01 as a decimal.

Now, using our calculator, follow these steps:

1. Enter 0.01 in the significance level input field
2. Click Calculate

The calculator returns the two-tailed z critical value as ±2.5758. Thus, at α=0.01, you can reject the null hypothesis if your test statistic is less than -2.5758 or greater than +2.5758.

Example 2. Right-Tailed Test

Find the z critical value for a right-tailed hypothesis test at a 5% significance level.

Solution

From the question, the significance level, α=5%, which is equivalent to 0.05 as a decimal.

To find the correct right-tailed z critical value for this test using our calculator, follow these steps:

1. Enter 0.05 in the significance level input field.
2. Click Calculate.

Since the calculator returns two-tailed, right-tailed, and left-tailed critical values, you need to select the correct critical value for your right-sided test.

From the calculator results, the right-tailed z-critical value at α = 0.05 is 1.6449. Thus, at 5% significance level, you can reject the null hypothesis if your test statistic is greater than 1.6449.

Example 3. Left-Tailed Test

Find the z critical value for a left-tailed hypothesis test at a 10% significance level.

Solution

From the question, the significance level (α) is 10%, which is equivalent to 0.10 as a decimal.

To find the correct left-tailed z critical value for this test using our calculator, follow these steps:

1. Enter 0.10 in the significance level input field.
2. Click Calculate.

The calculator returns two-tailed, right-tailed, and left-tailed critical values. In this case, you only need to select the correct critical value for your left-sided test.

From the calculator results, the left-tailed z-critical value at α=0.10 is -1.2816.

Thus, at a 10% significance level, you can reject the null hypothesis if your test statistic is less than -1.2816.

Want to learn how to look up z-tables for the correct critical values? Check out our complete guide on how to find z critical values from tables.

When to Use One-Tailed vs Two-Tailed Z Critical Values

The z critical value you choose depends on the direction of your hypothesis test. Before selecting a critical value, ask yourself whether your alternative hypothesis is looking for a difference in one specific direction or in either direction.

Use a two-tailed test when you want to test whether a value is significantly different from another value, but you are not specifying whether it should be higher or lower. In this case, the rejection region is split between both tails of the standard normal distribution.

For example, use a two-tailed test when your alternative hypothesis says: H_a​: μ ≠ μ₀​. This means you are testing whether the population mean is different from the hypothesized value.

Use a right-tailed test when you want to test whether a value is significantly greater than another value (H_a​:μ > μ₀​). In this case, the rejection region is in the right tail.

Use a left-tailed test when you want to test whether a value is significantly less than another value (H_a​:μ < μ₀). In this case, the rejection region is in the left tail.

Common Z Critical Values

While the calculator can give you exact results for any significance level, it is also helpful to have a quick reference. The table below shows the most widely used one-tailed and two-tailed z critical values at common significance levels.

Significance Level (α)	Confidence Level	One-Tailed	Two-Tailed
0.10	90%	1.282	±1.645
0.05	95%	1.645	±1.960
0.025	97.5%	1.960	±2.241
0.01	99%	2.326	±2.576
0.005	99.5%	2.576	±2.807
0.001	99.9%	3.090	±3.291

Related. How to find the z critical value in Excel

Frequently Asked Questions