Population

In 1791, Hempel noted the planet Earth's population to be "eight hundred million, give or take." (AUDIO: The Sword of the Chevalier)

In 2006, the Ninth Doctor claimed Earth's population to be five billion. (TV: World War Three)

Onboard the Titanic in 2008, the Tenth Doctor stated that the Earth's population was 6 billion. (TV: Voyage of the Dammed)

During the 456 crisis of 2009, Rick Yates acknowledged projections which predicted that Earth's population would reach nine billion by 2050, a two and a half billion rise. Soon after, Jack Harkness boasted that "over six billion angry human beings" would fight the 456. Denise Riley noted the Earth's population to be 6.7 billion people. (TV: Children of Earth: Day Four)

On Christmas Day 2009, a total of 6,727,949,338 people were temporarily transformed into the Master Race, constituting almost the entire human population of Earth save Donna Noble and Wilfred Mott, who were spared the transformation. (TV: The End of Time)

In 2010, 79B Aickman Road's autopilot noted that 17 potential pilots had been tried and that 6400000026 remained. Earlier that day, Sophie had estimated the total population at six billion. (TV: The Lodger)

In 2018, the Twelfth Doctor noted Earth's population to be seven billion. (TV: The Lie of the Land) In 2018 (TV: The Battle of Ranskoor Av Kolos) and early 2019, the Thirteenth Doctor approximated it at the same value. (TV: Resolution)

Later in the 21st century, Earth's population was 10 billion. (AUDIO: Hothouse)

By the year 2472, Earth's population was 100 billion. (TV: Colony in Space)

In the year 200,000, the Ninth Doctor noted Earth's population as being 96 billion. (TV: The Long Game)

New York City
In 1790, New York City's total population was 33,131. (TV: The Gathering)

In 1800, New York City's total population was 60,515. (TV: The Gathering)

In 1810, New York City's total population was 98,373. (TV: The Gathering)

In 1820, New York City's total population was 123,706, 5,390 of whom were foreign-born. (TV: The Gathering)

In 1830, New York City's total population was 202,583, 17,773 of whom were foreign-born. (TV: The Gathering)

In 1840, New York City's total population was 312,710. (TV: The Gathering)

In 1850, New York City's total population was 515,547, 235,733 of whom were foreign-born. (TV: The Gathering)

In 1860, New York City's total population was 813,669, 383,717 of whom were foreign-born. (TV: The Gathering)

In 1870, New York City's total population was 942,292, 419,094 of whom were foreign-born. (TV: The Gathering)

In 1880, New York City's total population was 1,206,209, 478,670 of whom were foreign-born. (TV: The Gathering)

In 1890, New York City's total population was 1,515,301, 839,347 of whom were foreign-born. (TV: The Gathering)

In 1900, New York City's total population was 3,427,202, 1,270,080 of whom were foreign-born. (TV: The Gathering)

In 1910, New York City's total population was 4,708,083, 1,044,257 of whom were foreign-born. (TV: The Gathering)

In 1920, New York City's total population was 5,620,042, 2,028,160 of whom were foreign-born. (TV: The Gathering)

In 1930, the population of New York City, or, as Charlotte Wills claimed, Manhattan, was 1,867,000. (TV: The Gathering)

In 1940, New York City's total population was 7,454,995, 2,138,657 of whom were foreign-born. (TV: The Gathering)

In 1950, New York City's total population was 7,891,957, 1,784,200 of whom were foreign-born. (TV: The Gathering)

In 1960, New York City's total population was 7,783,314, 1,558,690 of whom were foreign-born. (TV: The Gathering)

In 1970, New York City's total population was 7,824,756, 1,437,023 of whom were foreign-born. (TV: The Gathering)

In 1980, New York City's total population was 7,071,639, 1,670,199 of whom were foreign-born. (TV: The Gathering)

In 1990, New York City's total population was 7,322,554, 2,032,531 of whom were foreign-born. (TV: The Gathering)

In 2000, New York City's total population was 8,008,278, 2,871,032 of whom were foreign-born. (TV: The Gathering)

Charlotte Wills claimed that, around 2011, Manhattan had a population of less than 1,867,000, misreading the 1930 statistic as pertaining to just Manhattan. (TV: The Gathering)

Others
In 2007, Elton Pope claimed the population of London to be ten million. (TV: Love & Monsters)

In 2009, Rick Yates noted that the United Kingdom had a population of 61 million, which was projected to increase to 77 million by 2050. (TV: Children of Earth: Day Four)

In 2012, Henry van Statten noted Salt Lake City, the city nearest to his Vault, to have a population of one million. (TV: Dalek)

Other locations
At the time of its disappearance, Bandraginus V had a population of a thousand million. (TV: The Pirate Planet)

In the year 4000, the Solar System had a combined population of forty billion. (TV: The Daleks' Master Plan)

The City of the Saved was home to every human to ever live. The City's population was in the septillions and increased by 0.3 septillion each year. (PROSE: The Book of the War) The orientation material given to visitors of the City estimated the population was between 1024 and 1027 septillion, but the City census of AF 291 reported it was closer to 1038 septillion. (PROSE: Of the City of the Saved...)