Mathematics · Statistics
Lincoln–Petersen Capture–Recapture Population Calculator
Calculate estimated population size from product of first and second capture counts and recaptured marked count.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=a/b with product of first and second capture counts=2400 and recaptured marked count=24.
- estimated population size=100.
Understand Lincoln–Petersen Capture–Recapture Population
One idea, three depths
Choose how deeply to explain Lincoln–Petersen Capture–Recapture Population
Lincoln–Petersen Capture–Recapture Population: Calculate estimated population size from product of first and second capture counts and recaptured marked count.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Lincoln–Petersen Capture–Recapture Population to answer this question: calculate estimated population size from product of first and second capture counts and recaptured marked count? Enter product of first and second capture counts and recaptured marked count; the calculator shows estimated population size. For example: product of first and second capture counts=2400 and recaptured marked count=24 produce estimated population size=100. The answer tells you estimated population size.
Age 15Explain it to a 15-year-oldConnect it to the formula
The Lincoln–Petersen estimator divides the product of two capture-sample sizes by the marked recaptures. This page evaluates the relationship directly. The rule is c=a/b. Its input values are product of first and second capture counts, recaptured marked count, and the main result is estimated population size. For example: product of first and second capture counts=2400 and recaptured marked count=24 produce estimated population size=100.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated lincoln–petersen capture–recapture population relation over the valid real-number domain stated below. The implemented relation is c=a/b, evaluated from product of first and second capture counts, recaptured marked count to produce estimated population size. The Lincoln–Petersen estimator divides the product of two capture-sample sizes by the marked recaptures. This page evaluates the relationship directly. It assumes a closed population, equal capture probabilities, reliable marks, and independent capture occasions.
Inputs and valid domain
- product of first and second capture counts must be a finite real number.
- recaptured marked count must be a finite real number.
Important boundary: It assumes a closed population, equal capture probabilities, reliable marks, and independent capture occasions.
The formula
c=a/b
How the calculator works through it
It substitutes product of first and second capture counts, recaptured marked count into the formula and exposes every numerical step above. The main output is estimated population size.
Read the result correctly
The estimated population size is the direct answer to “calculate estimated population size from product of first and second capture counts and recaptured marked count.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
product of first and second capture counts=2400 and recaptured marked count=24 produce estimated population size=100.
Where this model stops being reliable
It assumes a closed population, equal capture probabilities, reliable marks, and independent capture occasions.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Lincoln–Petersen Capture–Recapture Population works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Lincoln–Petersen Capture–Recapture Population uses c=a/b. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Averages and representative values
Representative values help you judge what the Lincoln–Petersen Capture–Recapture Population inputs summarise and what the result can legitimately describe.
Review this foundation about 5 min
Optional enrichment
- Spread and measurement variation
Variation is not always part of the Lincoln–Petersen Capture–Recapture Population formula, but it helps you judge how stable a reported result may be.
Review this foundation about 6 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read product of first and second capture counts, recaptured marked count.
- Evaluate the principal relationship: c=a/b.
- Return estimated population size and check the domain conditions described above.
Python
from math import *
def lincoln_petersen_population_calculator(a, b) -> float:
return (a / b)
assert abs(lincoln_petersen_population_calculator(2400, 24) - 100) < 1e-6 * max(1.0, abs(100))
C
#include <assert.h>
#include <math.h>
double lincoln_petersen_population_calculator(double a, double b) {
return (a / b);
}
int main(void) {
const double expected = 100;
const double actual = lincoln_petersen_population_calculator(2400, 24);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double lincoln_petersen_population_calculator(double a, double b) {
return (a / b);
}
int main() {
constexpr double expected = 100;
const double actual = lincoln_petersen_population_calculator(2400, 24);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double lincoln_petersen_population_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global lincoln_petersen_population_calculator
section .text
lincoln_petersen_population_calculator:
push rbp
mov rbp, rsp
sub rsp, 32
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-8]
divsd xmm0, [rbp-16]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = lincoln_petersen_population_calculator(a, b)
result = (a / b);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := (a / b);
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
Introductory Statistics 2e
Read the free OpenStax statistics textbookCite this book
- APA 7
- Illowsky, B., & Dean, S. (2023). Introductory statistics 2e. OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction
- MLA 9
- Illowsky, Barbara, and Susan Dean. Introductory Statistics 2e. OpenStax, 2023, https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
- Chicago author-date
- Illowsky, Barbara, and Susan Dean. 2023. Introductory Statistics 2e. Houston, TX: OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Lincoln–Petersen Capture–Recapture Population Calculator. MW SysArc Tools. https://math.mwsysarc.com/statistics/lincoln-petersen-population-calculator
MLA 9
MW SysArc. “Lincoln–Petersen Capture–Recapture Population Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/statistics/lincoln-petersen-population-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Lincoln–Petersen Capture–Recapture Population Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/statistics/lincoln-petersen-population-calculator.
Harvard
MW SysArc (2026) ‘Lincoln–Petersen Capture–Recapture Population Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/statistics/lincoln-petersen-population-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_lincoln_petersen_population_calculator_2026,
author = {{MW SysArc}},
title = {Lincoln–Petersen Capture–Recapture Population Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/statistics/lincoln-petersen-population-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Lincoln–Petersen Capture–Recapture Population Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/statistics/lincoln-petersen-population-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Lincoln–Petersen Capture–Recapture Population do?
Calculate estimated population size from product of first and second capture counts and recaptured marked count.
How does the Lincoln–Petersen Capture–Recapture Population work?
The calculator applies c=a/b. The Lincoln–Petersen estimator divides the product of two capture-sample sizes by the marked recaptures. This page evaluates the relationship directly.
What can I learn from the Lincoln–Petersen Capture–Recapture Population?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .