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Sample Size for a Proportion — result sheet
Estimate how many observations a survey needs for a target proportion margin of error and confidence level.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: n₀ = z²p(1 − p)/E²; finite correction n = n₀ / (1 + (n₀ − 1)/N); round up.
Plan a simple random sample for estimating a population proportion. An optional finite-population correction reduces the requirement when the population is known and not large.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Planning proportion — Use 0.5 when no prior proportion is available; it is conservative.; minimum 0; maximum 1
- Margin of error — minimum 1.0E-6; maximum 1
- Confidence level — 3 choices
- Population size (optional) — Enter zero when the population is large or unknown.; minimum 0; maximum 1000000000000
Worked example
| Input | Value |
|---|---|
| Planning proportion | 0.5 |
| Margin of error | 0.03 |
| Confidence level | 95 |
| Population size (optional) | 0 |
1,068 observations needed before any nonresponse adjustment.
Assumptions and limits
- Simple random sampling and a two-sided normal approximation are assumed.
- Nonresponse, design effects, weighting, and subgroup oversampling are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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