Calculators
Capture–Recapture Calculator
Estimate a closed population with Chapman and Lincoln–Petersen capture–recapture methods, privately in your browser.
Estimate a closed population using two capture samples. Mark and release the first sample, then count marked individuals in the second sample. Enter whole counts up to 1000000; both samples must be positive. Marks must persist and individuals must mix with equal capture chances. Few recaptures give unstable estimates. All processing stays in your browser.
How capture–recapture population estimation works
Mark and release M individuals in the first sample. In a second sample of C individuals, count R marked recaptures. The Lincoln–Petersen estimate is M × C / R. The Chapman estimate is ((M + 1) × (C + 1) / (R + 1)) − 1, a correction often used to reduce small-sample bias. Its estimated variance is ((M + 1)(C + 1)(M − R)(C − R)) / ((R + 1)²(R + 2)); the standard error is the square root. For M = 100, C = 80 and R = 20, Chapman estimates about 388.571428571 individuals and Lincoln–Petersen estimates 400. The observed distinct count is M + C − R. These are estimates, not exact censuses, and fractional results are intentionally retained. The population must be closed between samples, marks must remain identifiable, marked individuals must mix fully, and capture chances must be equal. Births, deaths, migration, mark loss or capture avoidance can bias results. With zero recaptures the Lincoln–Petersen estimate is undefined; Chapman remains numerically finite but is unreliable. Few recaptures warrant caution. A zero estimated standard error at a boundary does not prove certainty. No confidence interval is inferred from the standard error. Counts must be whole numbers up to 1000000, both sample sizes positive, and R between zero and the smaller sample. Results use browser floating-point arithmetic with up to 12 significant digits. Inputs stay on your device.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What do the three counts mean?
M is the initially marked and released count, C is the entire second sample, and R is the marked subset of that second sample.
What happens with no recaptures?
Lincoln–Petersen divides by zero and is undefined. Chapman gives a finite number, but zero overlap makes the estimate unreliable.
Which assumptions are required?
A closed population, retained recognizable marks, adequate mixing and equal capture chances are required. Changes in population or capture behavior can bias results.
Is the estimate an exact population count?
No. It is a sampling estimate. Standard error describes estimated sampling variability and is not a confidence interval or guarantee.