Formula and calculation method
n₀ = z²p(1−p)/e². For population N: n = n₀/[1+(n₀−1)/N]. Round upward.
Normal-approximation sample size for a proportion with simple random sampling; not a power calculation. The critical z value is user-selected.
How to use sample size calculator
- Set Critical z value. The example below uses 1.96.
- Set Expected proportion (%). The example below uses 50.
- Set Margin of error (percentage points). The example below uses 5.
- Set Population size (0 = unlimited). The example below uses 0.
- Select Calculate to update the result. Reset restores the illustrated inputs. Copy, print or download your own result if you need a record.
Worked example
Example inputs
- Critical z value
- 1.96
- Expected proportion (%)
- 50
- Margin of error (percentage points)
- 5
- Population size (0 = unlimited)
- 0
- Required sample size
- 385
Inputs and results explained
Sample Size Calculator takes 4 inputs. Fill each one using the same units and conventions, then select Calculate.
- Critical z value: a number from 1e-06 to 10. The worked example uses 1.96.
- Expected proportion (%): a number from 0 to 100. The worked example uses 50.
- Margin of error (percentage points): a number from 1e-06 to 100. The worked example uses 5.
- Population size (0 = unlimited): a number from 0 to 1000000000000. Whole numbers only. The worked example uses 0.
The result panel reports Required sample size.
Factors affecting your result
Normal-approximation sample size for a proportion with simple random sampling; not a power calculation. The critical z value is user-selected.
Changing critical z value changes the scenario being evaluated. Adjust one input at a time when comparing results, keep a copy of the assumptions, and compare values using the same unit and period. A precise arithmetic result does not make an uncertain assumption precise.
Frequently asked questions
How does the sample size calculator work?
n₀ = z²p(1−p)/e². For population N: n = n₀/[1+(n₀−1)/N]. Round upward.
What inputs does Sample Size Calculator need?
Enter critical z value, expected proportion (%), margin of error (percentage points), population size (0 = unlimited). Read the unit labels; percentages are entered as ordinary percentages, not decimal fractions.
How should I interpret the sample size calculator result?
Normal-approximation sample size for a proportion with simple random sampling; not a power calculation. The critical z value is user-selected.
Are my sample size calculator inputs uploaded?
No. The calculation runs in this browser. Favorites, recent tool names, theme and formatting preferences may be saved locally, but calculation inputs are not sent to a calculation server or stored by this website. Shared links do not include entered values.
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