The territorial expansion in mentioned chronological boundaries (1770-1870) are nowhere close to trifle and heavily contributed to the population increase in that time. First and foremost, the Partitions of Poland that happened in three stages, in 1772, 1793 and 1795 allowed Russian Empire to annex substantial part of Poland and almost the entire Grand Duchy of Lithuania, what amounted to 462.000 square kilometers and 5.5 mln of inhabitants. Russian gains in the region increased again shortly after, when the Duchy of Warsaw established thanks to Napoleon became de facto Russian protectorate renamed to Kingdom of Poland in 1815 (that was eventually incorporated in 1832 as an autonomous region of the Empire). As the Duchy also included a substantial part of the territory annexed by Prussia during partitions and then lost to Russia in early 19th century, the population of the region gained by Russian Empire in the territories of the former Polish-Lithuanian Commonwealth was roughly 9.5 mln, i.e., almost 40% of the estimated population of Russian Empire in 1770s.

Furthermore, after annexation of parts of Finland in the first half of 18th century (Ingria, Livonia and part of Karelia in 1721 following the Treaty of Uusikaupunki, and additional part of Karelia in 1743 after the Treaty of Turku), Russians attacked Finland again during the Napoleonic Wars in 1808 to force it join the blockade. The war ended with the Treaty of Hamina in 1809 that allowed Russia to gain control over the entire territory of Finland.

Apart from Poland and Lithuania, a lot of territories annexed by Russian Empire were either small or sparsely populated, but they still added up to a non-negligible increase of population. In the discussed period, Russia managed to annex or incorporate e.g. Crimean Khanate (1780s), Georgia (1801-1812, with Swanetia and Megrelia being incorporated in 1859 and 1864, although these regions were already a Russian protectorate, eastern Armenia (1813-1828), Azerbaijan (1806), territory of modern Kazakhstan (1820s-1840s) and northern Uzbekistan (1860s). All this certainly contributed to the general population of the Empire.

According to the census of 1897, out of 125 mln of the inhabitants of Russian Empire, 22 million (17,6%) spoke 'Little-Russian' (Ruthenian, Ukrainian), 7.9 mln (6.32%) spoke Polish, 4.1 mln (3.3%) spoke Kazakh, 3.7 mln (3%) spoke Tatar or Azeri. This shows that taking into account only the largest groups inhabiting the territories annexed by Russian Empire on the discussed period, we can see that they amount to almost 1/3rd of the entire population of the latter.

In addition, although we can only rely on approximate conjectures due to lack of the comprehensive census data until late 19th century, it appears that Russia experienced a steady positive population balance of about 1.24% year to year (1012 births per each 1000 deaths) what might not seem too much, but after 100 years it amounts to an increase by almost 3.5 times. Even if one factors in occasional spells of hunger and war, this is more than enough to explain the rise of population. And please note that in the time we are speaking about, with a possible exception of the Napoleon's campaign of 1812, Russia did not experience any large-scale war that would have affected large part of its population (chiefly due to the sheer size of the country), so even the substantial losses of military personnel (over 450.000 in the case of Crimean War fought in 1853-1856) did not dent the population of the Empire to a large extent.

It might be conjectured that the increase of population could have been caused by the significantly rural character of Russian Empire, as in the rural families, that formed majority of the Imperial population, predominantly in Siberia, population growth was higher than average, especially in comparison with highly urbanized governorates of Petersburg, Livonia or Estland, while in large cities, like Moscow or St. Petersburg population in the second half of 19th century generally slightly decreased.

It should be also noted that the Russian population growth was not unique. England (not counting colonies, Scotland or Wales) experienced similarly quick population boom in the same period, with roughly 7.5 mln inhabitants around 1770 and 21.3 mln in 1871 (284% of the initial number). Population of Qing China rose from roughly 180 mln in 1750 to 430 mln in 1850 (238%). Sweden experienced growth of population from 1.78 mln in 1750 to 3.48 mln in 1850 (195%), despite the loss of Finland in early 1800s, and Netherlands increased its population from roughly 2 mln in 1800 to 5 mln in 1900 (250%).

Thus, the sudden increase of population between late 18th and laate 19th century is nothing unusual, as it matched the population increase in many other countries, and was further facilitated by substantial annexation of densely populated areas (mainly the eastern and central part of Polish-Lithuanian Commonwealth) and predominantly rural character of the country that contributed to a steady population growth.

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Rashin, A.G., Население России за 100 лет (1811-1913 гг.) [Population of Russia through 100 years (1811-1913)], State Statistic Office Publishing House, Moscow 1956