One-Proportion Z-Test Calculator
Compare a sample proportion with a stated reference value using the null standard error. The tool shows the method and key assumptions so you can inspect how the input values lead to the estimate.
How to use this calculator
- Enter observed successes using the unit and definition shown beside the input.
- Enter total trials using the unit and definition shown beside the input.
- Enter null proportion (%) using the unit and definition shown beside the input.
- Check that all values refer to the same time period and scenario.
- Review the outputs alongside the assumptions before using them in a decision.
Formula and assumptions
z=(p̂−p₀)/√(p₀(1−p₀)/n); approximate two-sided p-value uses the standard normal distribution.
- The normal approximation needs adequate expected successes and failures under the null. The tool does not correct for multiple comparisons or assess study design.
- The estimate is calculated from values you enter. It does not connect to external accounts, obtain live prices, or validate local regulations or engineering specifications.
Worked examples
Worked example
58 successes in 100 trials against a 50% null proportion gives z≈1.6 and a two-sided p-value near 0.11.
Enter integer counts and the null proportion as a percentage.
Use exact binomial methods when the normal approximation is unsuitable.
Understanding the result
The normal approximation needs adequate expected successes and failures under the null. The tool does not correct for multiple comparisons or assess study design.
Change one input at a time to see how sensitive the output is to that assumption.
Important notes
The normal approximation needs adequate expected successes and failures under the null. The tool does not correct for multiple comparisons or assess study design.
Frequently asked questions
What formula does the One-Proportion Z-Test Calculator use?
z=(p̂−p₀)/√(p₀(1−p₀)/n); approximate two-sided p-value uses the standard normal distribution.
What should I verify before relying on the result?
The normal approximation needs adequate expected successes and failures under the null. The tool does not correct for multiple comparisons or assess study design.
Can I compare different scenarios?
Yes. Change one assumption at a time, keep units and definitions consistent, and save the inputs used for each comparison.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate Percent Error — Learn the percent error formula and how to compare an experimental value with a reference or accepted value.
- How to Calculate Standard Deviation — Learn what standard deviation measures, the population and sample formulas, and how to interpret the result.
- Standard Deviation — Understand standard deviation as a measure of spread and the difference between population and sample standard deviation.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.