Z-Test Calculator
One-sample z-test with p-value and confidence interval.
Enter your values
ⓘ Live results
Results
- z statistic
- 1.6
- p-value (two-tailed)
- 0.1096
- p-value (one-tailed)
- 0.0548
- Verdict
- Not significant at the 5% level
- Standard error
- 2.5
- 95% CI for the mean
- 99.1 to 108.9
Quick answer
The z-test uses z = (x̄ − μ) ÷ (σ ÷ √n) when the population standard deviation is known, comparing z against the normal distribution.
z = (x̄ − μ) ÷ (σ ÷ √n)
How to use the Z-Test Calculator
- 1Enter your sample mean and sample size.
- 2Enter the population mean you are testing against and the known population SD.
- 3Read the two-tailed p-value unless you have a directional hypothesis stated in advance.
Worked example
Using the values the calculator loads with:
Inputs
- Sample mean104
- Population mean μ100
- Population SD σ15
- Sample size36
Results
- z statistic1.6
- p-value (two-tailed)0.1096
- p-value (one-tailed)0.0548
- VerdictNot significant at the 5% level
- Standard error2.5
- 95% CI for the mean99.1 to 108.9
Frequently asked questions
z-test or t-test?
Use z when the population SD is genuinely known — rare outside textbooks and quality control. Otherwise use a t-test.
Is n = 30 the cutoff?
It is a rule of thumb for normality of the sampling distribution, not a licence to ignore an unknown sigma.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.