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A demographer studies human populations quantitatively: how many people are present, how their characteristics are distributed, and how births, deaths and human migration change those counts. The work connects population census definitions and statistical sampling to statistical estimation and mathematical models of population dynamics. A forecast must distinguish observed counts from assumptions about future rates.^[ref]

For example, in a closed demographic cohort with $n_a(t)$ people aged $a$ and common one-year survival probability $s_a(t)$ conditional on that count, a basic projection isA cohort of 1000 people with survival probability $0.998$ contributes an expected 998 survivors to the next age class. Births create a new youngest class, and human migration requires additional terms. This elementary calculation illustrates why a demographer works with age structure and explicit statistical parameters, rather than extrapolating a single total without assumptions.

For a fixed territory and interval, the demographic balancing equation is the accounting identitywhere $N_0,N_1$ are initial and final resident counts and $B,D,I,E$ are births, deaths, immigration and emigration during that interval. All quantities must use compatible definitions of territory, residence and reference time. This is conservation of population counts, not an assumed law of population dynamics.

For $N_0=10000$, $B=140$, $D=90$, $I=80$ and $E=110$, the final count is $10020$: natural increase adds 50 and net human migration removes 30. Rearranging yields $I-E=N_1-N_0-B+D$, allowing net migration to be estimated residually. In measured data, that residual also absorbs errors in censuses and vital-event counts, so the identity does not independently establish the accuracy of any measurement.

A demographic cohort is a group defined by experiencing a specified event during the same interval, then followed through time. A birth cohort consists of people born in a stated period; other examples group people by year of immigration or first diagnosis. It is not the same as all people of a given age in a single cross-section.

Ignoring migration, a birth cohort with 1000 initial members and 950 survivors ten years later has ten-year survival proportion $950/1000=0.95$. Comparing that with the proportion of today's ten-year-olds among today's residents answers a different question, because births, deaths and human migration have affected the denominator. Cohort analysis separates changes experienced by a group as it ages from changes between successive groups. For a cohort defined by birth year $c$, calendar year and age satisfy $t=c+a$, which creates an exact dependence in attempts to estimate age, period and cohort effects simultaneously.

Demography measures the size, composition and change of human populations. It combines population censuses, registrations of births and deaths, and statistical sampling with mathematical models of population dynamics. A population census refers its counts to a specified time and territory; collecting questionnaires on different days should not silently change the reference date.^[ref]

For a fixed territory, a demographic accounting identity iswhere $B,D,I,E$ count births, deaths, immigration and emigration during the intervening period. For example, $N(t_0)=10000$, $B=140$, $D=90$, $I=80$ and $E=110$ give $N(t_1)=10020$. This demographic balancing equation distinguishes natural increase from net human migration; it does not assume an exponential growth law.

Counts also need denominators. A birth rate compares births with the relevant population exposure, rather than comparing raw birth totals between differently sized human populations. Changes in age composition can alter an aggregate rate even when the underlying age-specific rates remain fixed, motivating analysis by demographic cohorts.

For demography, human migration is movement that changes a person's place of usual residence across a specified territorial boundary. Counts depend on the boundary, the residence criterion and the observation interval. A commuter crossing daily and a person changing residence therefore need not be counted alike.

In the demographic balancing equation, immigration $I$ adds residents and emigration $E$ removes them, so net migration is $I-E$. If a district gains 800 and loses 500 residents by migration during a year, its net migration is 300, while the total number of moves is 1300. Net migration alone can conceal substantial turnover. Movement between two districts contributes to each district's account but cancels in the national total if both districts are inside the same national boundary. This accounting viewpoint is the quantitative aspect used here.

Thomas Robert Malthus made the comparison between population growth and the growth of food supply explicit in his 1798 An Essay on the Principle of Population by Thomas Robert Malthus. In Chapters I–II, he assumed that unchecked numbers could follow a geometric progression, taking doubling every 25 years as his rule, while food supply gained a fixed amount in each such period, an arithmetic progression. These were different hypotheses about two quantities, rather than a calculation from a single universal growth law.^[ref]

With equal initial scales, his comparison can be written as $N_k=N_0{2}^k$ and $F_k=F_0(1+k)$ after $k$ periods of 25 years. Then $N_k/F_k=(N_0/F_0)2^k/(1+k)$ grows without bound. The corresponding continuous exponential growth rate for numbers would be $\log (2)/25$ per year. The mathematics describes the consequence of the assumed rates; it does not establish that actual birth, death, human migration and food-production rates stay fixed. Demography can test population assumptions against counts, age composition and measured rates.