Population Pyramids: Projecting a Nation's Age Structure Forward

A population is a stack of cohorts

A population pyramid is a snapshot: two back-to-back horizontal bar charts, one sex on each side, one bar per age group, stacked from newborns at the bottom to the oldest survivors at the top. The shape of that stack — a wide triangle, a rectangle, or an urn narrower at the base than the middle — is a fingerprint of a country's birth rate, death rate and history, and projecting it forward is one of the oldest and most reliable exercises in demography.

The cohort-component model

The standard projection method ages the population one year at a time using three separate processes. First, survival: each age-sex cohort shrinks according to age-specific survival probabilities taken from a life table, low in infancy, near 1 through most of adulthood, falling steeply past 60. Second, fertility: births come from age-specific fertility rates (ASFR) applied to the female cohorts of reproductive age, roughly 15-49. Third, migration, which can add or remove people from any cohort independently of birth and death.

P(a+1, t+1) = P(a, t) . S(a)                    // survivors age by one year
B(t)       = sum_a  ASFR(a) . P_female(a, t)     // total births this year
P(0, t+1)  = B(t) . SRB / (1 + SRB) . S(0)        // newborns split by sex ratio at birth
TFR        = sum_a  ASFR(a)                       // total fertility rate, "births per woman" 

Run those three rules forward one year, shift every surviving cohort up one row, drop a new row of newborns at the base, and you have next year's pyramid. Run it for eighty years and you have a full-population projection — the same method national statistics offices use, just with far more age brackets and separate rates by region.

Reading the shape

Three archetypal shapes recur worldwide. An expansive pyramid is a wide-based triangle: total fertility rate (TFR) well above the replacement level of about 2.1 children per woman, each cohort bigger than the one above it, a young median age and a high dependency ratio driven by children. A stationary pyramid is closer to a rectangle: fertility near replacement, roughly equal cohort sizes until mortality thins the oldest ages, a stable population size. A constrictive (or 'urn') pyramid narrows at the base: sub-replacement fertility for long enough that each new cohort is smaller than its parents', a rising median age, and eventually a shrinking population unless offset by immigration.

The dependency ratio — the ratio of the population outside working age (typically under 15 and over 64) to the population inside it — falls out directly from the pyramid's shape and drives a lot of policy: pension systems, school capacity, healthcare demand. A pyramid moving from expansive to stationary passes through the so-called demographic dividend, a period when the working-age share peaks and dependency is at its lowest, before population ageing pushes it back up.

Why shape lags rate changes by decades

The pyramid's momentum is the trap that catches most intuitive forecasts: even after fertility drops sharply to replacement level, a population with a young age structure keeps growing for another generation or two, simply because there are more women about to enter childbearing age than there are women currently in it. This effect, population momentum, is why fertility can fall below replacement for years before total population growth actually turns negative — and why the pyramid, not the birth rate alone, is the number demographers watch.

Frequently asked questions

Try it live

Everything above runs in your browser — open Population Pyramid and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.