Sample size calculator for a population proportion
Choose confidence, margin of error, expected proportion and optional population size. HitEquals returns the minimum completed sample, unadjusted size, finite-population correction and nonresponse scenarios.
Inputs used by this calculator
Sample Size Calculator uses the fields below. The starting values reproduce the page example; replace them with values from the same units and time period before using the result.
| Input | Starting example | Accepted value | How it is used |
|---|---|---|---|
| Confidence level | 95% | 90% · 95% · 99% | Supplies the confidence level quantity used by the published equation or result breakdown. |
| Margin of error (%) | 5 | 0.01 to 50 | Supplies the margin of error (%) quantity used by the published equation or result breakdown. |
| Expected proportion (%) | 50 | 0.01 to 99.99 | Supplies the expected proportion (%) quantity used by the published equation or result breakdown. |
| Population size (0 = very large) | 0 | 0 to 1000000000000 | Supplies the population size (0 = very large) quantity used by the published equation or result breakdown. |
| Design effect | 1 | 0.1 to 100 | Supplies the design effect quantity used by the published equation or result breakdown. |
What this sample size estimates
The result plans estimation of one population proportion using a two-sided normal approximation and simple random sampling.
Core proportion formula
The most conservative planning value is p=0.5 because p(1−p) is largest there.
n₀=z²p(1−p)/e²Finite population correction
When sampling a meaningful fraction of a known finite population, the correction reduces the required completed sample.
n=n₀/[1+(n₀−1)/N]Worked 95% example
With z≈1.96, p=0.5 and e=0.05, n₀≈384.15, which rounds upward to 385 completed responses.
Design effect and nonresponse
A design effect inflates the effective sample for clustering or unequal weights. Nonresponse scenarios show how many invitations may be needed but are not included in the primary completed-sample result.
When this formula is insufficient
Small expected counts, complex surveys, paired designs, multiple primary outcomes and hypothesis tests need a design-specific power analysis.
Common two-sided normal critical values
| Confidence | z critical |
|---|---|
| 90% | 1.64485 |
| 95% | 1.95996 |
| 99% | 2.57583 |
Frequently asked questions
Why is 50% the default proportion?
It produces the largest variance and a conservative sample when the true proportion is unknown.
Should sample size be rounded up?
Yes. A partial respondent cannot satisfy the target.
What does population zero mean?
The population is treated as very large, so no finite-population correction is applied.
Does this include nonresponse?
The main result is completed responses; invitation scenarios are shown separately.
What is design effect?
An inflation factor for variance from complex sampling relative to simple random sampling.
Is this a statistical power calculator?
No. It plans precision for one proportion.
What to keep in mind
This planning formula targets one proportion under a normal approximation and completed simple-random responses. Add expected nonresponse separately; clustering, weighting, subgroup estimates and rare outcomes need study-specific design.
Results are rounded for display in US format, with money in dollars and cents; CSV exports keep full calculation precision. This is a calculation summary, not an official certificate.