Mark-Recapture Population Calculator
Mark-recapture estimates how many animals live in an area without counting them all. You mark a first sample, release them, then take a second sample and see what fraction is already marked. That fraction scales up to a total population estimate. This calculator reports both the classic Lincoln-Petersen index and the bias-corrected Chapman estimator, which is usually preferred. Enter the number marked, the second-sample size, and the number recaptured. Both formulas are exact; the estimate's reliability depends on the closed-population assumptions.
Mark-recapture formulas
Lincoln-Petersen: N = M * C / R
Chapman: N = ((M + 1) * (C + 1) / (R + 1)) - 1
M = marked first, C = second sample size
R = marked animals recaptured in second sample
With M = 80, C = 100, R = 20: Lincoln-Petersen gives 80 times 100 over 20 = 400, and Chapman gives (81 times 101 / 21) minus 1, about 388.6.
Field study facts
- The method assumes a closed population between the two samples.
- Marks must persist and not change an animal's survival or catchability.
- Every individual should have an equal chance of capture.
- The Chapman estimator reduces bias, especially for small samples.
- Very few recaptures make the basic index unstable.
Mark-recapture: frequently asked questions
How does mark-recapture estimate a population?
You capture and mark a number of animals, release them, then later take a second sample. The proportion of marked animals in the second sample reflects the proportion of marked animals in the whole population, which lets you scale up to a total population estimate.
What is the Lincoln-Petersen index?
The Lincoln-Petersen index estimates population as N = M times C divided by R, where M is the number marked in the first sample, C is the total caught in the second sample, and R is how many of the second sample were already marked. It is the simplest mark-recapture estimator.
What is the Chapman estimator?
The Chapman estimator is a bias-corrected version: N = ((M plus 1) times (C plus 1) divided by (R plus 1)) minus 1. It is less biased than the basic Lincoln-Petersen index, especially for small samples, and is generally recommended for field studies.
What assumptions does mark-recapture make?
It assumes the population is closed (no births, deaths, immigration, or emigration between samples), that marks are not lost and do not affect survival or catchability, and that every animal has an equal chance of capture. Violations bias the estimate.
Why can the basic index be unreliable with few recaptures?
If the number of recaptured marked animals R is very small or zero, the Lincoln-Petersen index becomes unstable or undefined, because dividing by a tiny number inflates the estimate. The Chapman estimator adds one to each term, which keeps it defined and reduces this bias.
Official sources
- USGS: USGS population estimation methods.
- U.S. Fish and Wildlife Service: USFWS wildlife survey resources.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.