Mark–Recapture Population Calculator
Estimate a closed population from two samples and their marked overlap. Compare the school proportion estimate with the Chapman correction and the observed minimum.
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Result
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Calculation steps
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How to calculate
Assume the marked share in the second sample represents the marked share in the whole population. SolveM/N≈m/n. The Chapman correction changes all three counts by one before subtracting one from the final ratio.
Lincoln–Petersen N≈Mn/m; Chapman N≈(M+1)(n+1)/(m+1)−1
Worked example
Mark100 objects, then sample80 and find20 marks. The proportion estimate is400; the Chapman estimate is about388.571. At least100+80−20=160 distinct objects were observed.
Assumptions and input details
Counts are positive integers≤1e9, and recaptured marks cannot exceed either sample. Zero recaptures are rejected because the elementary ratio has no finite estimate. Population must remain closed, marks must persist, and sampling/mixing must give comparable capture chances. No confidence interval is inferred from two counts.
References: NOAA mark–recapture estimators
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.
Is my input uploaded?
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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