How to use the power analysis calculator
Prepare the values for this calculation
Estimate sample size for a two-sided one-sample mean test using a normal approximation and standardized effect size. Use the formula below to check that it answers your question. Read the input units before transferring figures from a statement, measurement or dataset.
Enter and check each input
- Standardized effect size |d|: enter a value at least 1e-06. Use the unit named in the label or selected above. Do not leave this required field blank.
- Significance level α: enter a value at least 1e-06 and no more than 0.5. Use the unit named in the label or selected above. Do not leave this required field blank.
- Target power: enter a value at least 0.500001 and no more than 0.999999. Use the unit named in the label or selected above. Do not leave this required field blank.
The input table gives a complete example. Keep units and time periods consistent across related fields.
Calculate and resolve any input error
Choose Calculate after entering the values. Changes also update the answer after a short pause. If an error appears, follow its message, correct the field and calculate again. Reset restores the example values.
Interpret the answer
Check Approximate required sample size first. With the unchanged example inputs, it is 32. Compare the additional metrics with the primary result; each has its own label and unit.
Compare and keep a useful result
For a controlled comparison, keep every other example input unchanged and change Standardized effect size |d| from 0.5 to 0.6. The resulting Approximate required sample size is 22. This illustrates the equation’s response to that input, rather than a forecast of real events.
Read the chart’s axis labels and data table. A scenario curve changes one stated input while holding the others fixed; it does not add external observations. Use Download graph to save an available chart as a PNG.
Use Copy result or Download CSV to keep the answer. Share tool shares the page address without placing your input values in the URL. Recheck inputs and assumptions before using the result for a decision.
Power Analysis Calculator formula
n≈[(z₁₋α/2+z_power)/d]².
Inputs and units
| Input | Format / range | Example |
|---|---|---|
| Standardized effect size |d| | minimum 1e-06 | 0.5 |
| Significance level α | minimum 1e-06; maximum 0.5 | 0.05 |
| Target power | minimum 0.500001; maximum 0.999999 | 0.8 |
Worked example
Using the example inputs above, the approximate required sample size is 32.
- Approximate required sample size
- 32
- Unrounded n
- 31.395519
- z(1−α/2)
- 1.959964
- z(power)
- 0.841621
Results and assumptions
Normal-approximation planning formula for a standardized one-sample mean effect.
Fix an input or unexpected result
Standardized effect size |d| is required. Enter standardized effect size |d| using the format and bounds in the input table. Zero and an empty field are different: use zero only if it is allowed and represents your data.
If your answer differs from the example, choose Reset and compare every field, including selected units and options. Check percentage versus decimal entry and whether values describe the same period. Round only the final displayed answer when reproducing the formula.
If a discrepancy remains, report the calculator issue with the page address, non-sensitive example inputs, actual result, expected result and a reference for your calculation.