Survey Population Estimate Calculator
Project a sampled proportion to a known population. Compare the estimate with the logically possible count range and, for small sample fractions, a Wilson sampling interval.
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Result
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Calculation steps
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How to calculate
Usek/n as the estimated population proportion, then multiply byN. The observations alone allow as few ask total successes or as many ask+N−n. For random independent or approximately independent sampling, an approximate Wilson interval describes sampling uncertainty.
Estimated count=Nk/n; possible count range=[k,k+N−n]
Worked example
40 successes among100 randomly selected people from10000 gives an estimate of4000. The95% Wilson proportion interval is approximately30.94%–49.80%; it does not account for nonresponse or selection bias.
Assumptions and input details
Use integer0≤k≤n≤N≤1e9. Sampling is assumed random, unique and equally weighted. The binomial Wilson approximation is shown only whenn/N≤10%; for larger fractions use a finite-population method. A complete census has an exact count. Projected interval endpoints are estimates, not guaranteed bounds; the separate possible range is guaranteed by the observed counts alone. This is an introductory sampling extension beyond basic proportion arithmetic.
References: NIST Wilson proportion intervals
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
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The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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