Sample Size for Proportion Calculator
Find how many respondents you need to estimate a population proportion within a target margin of error at a given confidence level.
Confidence level
Assumes a very large / infinite population
- 1
Proportion variance p(1 − p)
0.5 × (1 − 0.5) = 0.25 - 2
Numerator z*² × p(1 − p)
1.96² × 0.25 = 0.9604This is the numerator of the sample-size formula. - 3
Raw sample size n₀
0.9604 ÷ 0.05² = 384.16 - 4
Required sample size (round up)
385n₀ rounded up to the nearest whole number.
How does this calculator work?
To size a proportion survey, use n = z*² · p(1 − p) / E², where z* is 1.645, 1.96, or 2.576 for 90%, 95%, or 99% confidence. Use p = 0.5 when unknown for the most conservative estimate, round up, and apply the finite-population correction if you know your population size.
Formula
How this is calculated
The confidence level sets the critical z-value (z*): 90% → 1.645, 95% → 1.96, 99% → 2.576. A higher confidence level uses a larger z* and therefore demands a larger sample. The expected proportion p is your best guess of the share with the trait of interest (between 0 and 1). The margin of error E is the half-width of the confidence interval you can tolerate, expressed as a decimal (0.05 means ±5 percentage points).
The core formula n = z*² · p(1 − p) / E² comes from inverting the standard error of a proportion. The product p(1 − p) is maximized at p = 0.5, so when p is unknown, using 0.5 gives the most conservative (largest) sample size — guaranteeing your margin no matter the true value. The raw n is always rounded up with ceiling, since you cannot survey a fraction of a person.
If you supply a finite population size N, the finite-population correction n′ = n / (1 + (n − 1)/N) shrinks the requirement because sampling without replacement from a small population is more efficient. Leave N blank to assume an effectively infinite population. Note that E must be greater than 0, and p is clamped to the valid 0–1 range (falling back to 0.5 otherwise).
Frequently asked questions
Because p(1 − p) is largest at p = 0.5, it yields the maximum required sample size. Using it guarantees your margin of error will be met regardless of the true proportion, so it is the safe default.
Enter it as a decimal. A ±5% margin is 0.05, and ±3% is 0.03. Smaller margins require dramatically larger samples since n scales with 1/E².
It matters when your population is small relative to the computed sample size. For large populations the correction is negligible, but for a few hundred or thousand it can meaningfully reduce the sample you need.
Also known as
TG we-Calculate Editorial Team. (2026). Sample Size for Proportion Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/sample-size-for-proportion-calculator
TG we-Calculate Editorial Team. "Sample Size for Proportion Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/sample-size-for-proportion-calculator.
TG we-Calculate Editorial Team, "Sample Size for Proportion Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/sample-size-for-proportion-calculator
@misc{wecalculate_sample_size_for_proportion_calculator, title = {Sample Size for Proportion Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/sample-size-for-proportion-calculator}}, year = {2026}, note = {TG we-Calculate} }
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