How these numbers are produced

The short version

Births are estimated as population × crude birth rate ÷ 1,000. That is not an approximation — it is the definition of the crude birth rate. All the difficulty is in knowing the two inputs, and how well they are known changes enormously depending on the year.

The birth-rate model, before 1800

No source records births anywhere in the world before the 19th century, so for those years the birth rate has to be reconstructed. The obvious shortcut — pick one historical birth rate and apply it everywhere for eighteen centuries — would make the map a population map wearing a different label. Instead the rate comes from stable-population theory.

In a population growing at a steady rate r, where p(a) is the chance of surviving from birth to age a, the crude birth rate is fixed by an identity rather than an assumption:

b = 1 / ∫ e−ra p(a) da

This is exact for a stable population, and pre-industrial populations are close to stable over the century-scale steps the population data actually resolves. When growth is zero it reduces to the familiar b = 1/e₀: a society where people live 25 years on average must have about 40 births per 1,000 people a year simply to still be there.

Two things feed it, and neither is invented:

• Growth rate. Measured directly from the population series being explained, between the stored years on either side. So a country whose population was growing gets a higher birth rate than one whose was not — which is where the country-to-country variation before 1800 comes from.
• Survivorship. Averaged from 17,466 real UN life tables, grouped by life expectancy, covering e₀ from 26 to 86. Years of famine, genocide and epidemic are excluded, because their age patterns are nothing like a settled historical population. Below e₀ 26, where the UN panel runs out, the nearest observed age pattern is borrowed and rescaled so that it sums to the target life expectancy exactly.

The one genuine assumption

Life expectancy before 1800 is not known for most of the world. The map assumes 25 years everywhere before 1600, which is the range the demographic literature converges on for pre-modern populations, and then ramps onto the first attested regional figures by 1800 — 33.3 years for Europe, 28.5 for the rest of the world, from Riley's reconstruction.

A single global value is used rather than invented regional differences, because the evidence does not support them. Moving that assumption by ±3 years moves every pre-1800 birth estimate by about 13%. That figure is measured from the model, not guessed, and it is folded into the uncertainty shown on every pre-1800 value.

What the model gets wrong

At 1800 the model and Gapminder both produce a birth rate for the same country by completely separate reasoning — ours from mortality and growth, Gapminder's from historical demographic sources. That overlap is the only empirical test this model can be given, so here is the result, whether or not it flatters the method.

• 18%median error across 191 countries
• 73%within 30% of Gapminder
• 56%within 20%
• -11.1%average bias — the model runs low

Read that honestly: a typical country's modelled 1800 birth rate is about a fifth away from the independent reconstruction, and the model runs systematically low. The low bias has a plausible cause — by 1800 mortality was already falling in several countries, which makes a population younger than stable theory assumes and pushes its real birth rate above the stable value. No correction is applied for it. Fitting the pre-1800 series to match Gapminder at 1800 would assume the same disequilibrium held in the year 500, which contradicts the premise the model rests on, and would turn an independent estimate into a copy of another dataset.

The modelled series is, however, tapered onto the first reconstructed value across the 18th century, so the animation does not step at 1800 — a year in which nothing demographic happened. The median size of that join is about 11%.

Borders, and what a country means before it existed

Every figure on this map is for the land inside a country's present-day borders. "France in the year 800" means the area that is France today — not the Carolingian Empire, and not any polity that existed then. HYDE reconstructs population on a grid and sums it inside modern boundaries, and that is what the map shows.

This is a real limitation, stated rather than hidden. The alternative — drawing historical polities and assigning births to them — would require year-by-year boundary data and population estimates attributed to those boundaries, and for most of the world before 1500 neither exists at a quality that would justify the extra precision it implies. Choosing a consistent geography and saying so is the more defensible option; the map displays a standing warning whenever the year is before 1800.

Years between the evidence

The population reconstructions resolve centuries before 1500, decades through the 1700s, and years from 1800. The map stores exactly those years — 258 of them — and nothing finer, because storing annual values for the year 743 would be inventing detail no source contains.

Playback fills the gaps by interpolating: population geometrically, because populations compound, and birth rates linearly. Any year produced this way is labelled interpolated in the interface. It is an animation convenience, not evidence.

How much to trust a number

Population error and birth-rate error are independent, so they are combined in quadrature. The population terms reflect how far the major reconstructions diverge from one another for each period; the birth-rate term for the modelled era is measured from the model itself.

Numbers are printed to the precision their uncertainty supports and no further. A modelled estimate is shown as ~9.3 million, never as 9,304,187 — the extra digits would be decoration, and decoration that looks like evidence.

Known weaknesses

• Before 1800 the spread of birth rates between countries is narrow, because the only thing driving it is population growth. The map is, for those years, close to a population map — and that is a fair reading of what the evidence supports, not a bug being hidden.
• Several countries carry a single Gapminder birth rate across long stretches of the 19th century. Year-to-year detail there is not real.
• Migration is not separated out. The growth rate feeding the model is total population change, so for places shaped by large migrations — the Americas after 1500 above all — the modelled birth rate absorbs movement that was not births.
• 2026 has not happened. It is the UN's medium-variant projection.

See every source