Statistics

Confidence Level Z Value Tool

Convert confidence levels to z critical values and margin of error.

Last validated: 2026-02-14

Confidence Level Z Value Tool maps common confidence levels to corresponding normal critical z-values. It is useful when building confidence intervals and hypothesis tests manually. The tool removes lookup-table friction during calculations. Use it as a quick reference utility in statistical workflows.

Permalink

Input Pattern

Enter values in the left panel, keep units explicit, run the calculation, then copy or share the result. Invalid fields are highlighted immediately.

Confidence Inputs

Result

Alpha: 5.0000%

Critical z*: 1.95996399

Margin of error: 2.93994598

How to use this tool

Enter or select the confidence level.
Run the tool to retrieve the matching z critical value.
Use that value in interval or margin-of-error formulas.

Worked Example

Auto-generated from the tool's current default or entered inputs.

Example Inputs

Confidence percent: 95.0
Sigma: 15.0
Sample size: 100
Alpha percent: 5.000000000000004
Z value: 1.959963986120195
Margin of error: 2.9399459791802927

Expected Outputs

Confidence percent: 95
Sigma: 15
Sample size: 100
Alpha percent: 5

Interpretation

Confidence percent is 95.0. Use this as a decision input, not as a standalone conclusion.
Sigma is 15.0. Use this as a decision input, not as a standalone conclusion.
Sample size is 100. Use this as a decision input, not as a standalone conclusion.
Interpret this value alongside sample quality and assumptions to avoid overconfidence.

Scenario Compare (A vs B)

Use this to compare two input sets and quantify change in key outputs.

Scenario A

Confidence percent

Sigma

Sample size

Alpha percent

Z value

Margin of error

Scenario B

Confidence percent

Sigma

Sample size

Alpha percent

Z value

Margin of error

Confidence and limitations

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Interpretation depends on assumptions (distribution, independence, sample quality).

Formula References

Frequentist estimation and hypothesis-test formulas used in standard textbooks.
Interpretation depends on sample quality and assumptions.

Assumptions

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Interpretation depends on assumptions (distribution, independence, sample quality).

Explore more versions

Tailored guides for specific audiences, regions, and scenarios.

core