Z Test Calculator
Enter a sample mean, population mean, known population standard deviation and sample size to get the z statistic and its two-tailed p-value, with a note on significance at the 0.05 level.
What this calculator does
The Z Test Calculator estimates your result instantly from the values you enter, using standard statistics formulas. Enter a sample mean, population mean, known population standard deviation and sample size to get the z statistic and its two-tailed p-value, with a note on significance at the 0.05 level. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.
Result
About Z Test Calculator
This calculator runs a one-sample z test for a mean when the population standard deviation is known. Enter the sample mean, the population mean (μ₀), the population standard deviation (σ) and the sample size, and it returns the z statistic and the two-tailed p-value.
Use it for large-sample or known-variance situations; the result note tells you whether the outcome is significant at α = 0.05.
Formula & Mathematical Calculation
Z Statistic = f(Sample mean, Population mean (μ₀), Population std. deviation (σ), Sample size (n))
Calculated according to standard stats formulas implemented in the calculator core.
Calculation Example
Enter a Sample mean of 52, a Population mean of 50, a Population std. deviation of 6 and a Sample size of 40, then click Calculate.
The tool returns Z Statistic = 2.1082 and Two-tailed P-Value = 0.035015, with the note: “Z = 2.1082, two-tailed p-value = 0.035015. Significant at α = 0.05.”
Key Benefits
- Calculates the z statistic for a sample mean against a population mean with known standard deviation
- Returns the two-tailed p-value using a built-in normal distribution approximation
- States directly whether the result is significant at the 0.05 level
- Rejects a non-positive standard deviation or a sample size below 1 before calculating
How to Use this Calculator
-
Enter the sample mean
Type your observed sample average into the Sample mean field. -
Enter population parameters
Type the population mean and the known population standard deviation (greater than 0). -
Enter the sample size
Type the number of observations (at least 1) into the sample size field. -
Calculate and read
Click Calculate, then read the Z Statistic box, the Two-tailed P-Value box and the significance note.
Assumptions & Limitations
What the calculation assumes
- Every value you enter is treated as an exact, known amount.
- Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
- Results use standard published formulas and account only for the values entered above.
- Rounding is applied for display; the underlying calculation uses your full precision.
- Results are returned in the same units you enter, unless the tool states the output unit.
What it does not cover
- Z Test Calculator produces a calculated result for reference and learning, not a certified or official measurement.
- Real-world outcomes differ when tolerances, rounding rules or local standards apply.
- Definitions and standards vary by region and change over time; verify the convention that applies to your case.
- Figures are only as accurate as the inputs you supply — check them before acting on the result.
- For work where the result carries real consequences, confirm it against an authoritative source.
Frequently Asked Questions
Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.