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This article states:

To put it in broader perspective, Muslim population has steadily grown from 13% in 1800 to 16% in 1850 to 20% in 1900 to 25% in 1947 and anywhere between 30 to 33% today taking into account the geographical area of pre-partitioned India. These statistics are available from various sources.

It doesn't provide any reference that I can check.

This book estimates that India's population may have been 185 million in 1800 AD.

Muslim population in 1800 AD

But it doesn't give any estimate of the Muslim population.

13% of 185 million = 24.05 million. Is it a correct estimate?

According to most widely accepted estimate by historians, What was the population of Muslims in the Indian subcontinent in 1800 AD?

(If such data is not available, I would be happy with estimates of between 1800 and 1850)

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India's first (& most reliable) census was from 1867 to 1871, known as the 1872 Census of India. The Government of India confirms this in their census history. So, there is no data prior to this census, hence all numbers below are estimates.

In terms of estimated population, circa 1800 to 1850, The Cambridge Economic History of India, Volume 2, c.1751–c.1970 provides estimates on p.466, Table 5.1 (the range is from different authors' estimates):

  • 1800: 157 to 214 million
  • 1850: 183 to 247 million

I cannot find any information on estimates of Muslim population circa 1800 to 1850, but hopefully the range of total population might come in useful.

Your estimated Muslim population of 13% is extremely close to the Government of India's (2001 Census Data) estimate: 13.4%.

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    Upvote for splendid research, summary and answer. – MCW Sep 5 '17 at 15:53
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    Thanks, I was actually surprised I couldn't get better sources on Muslims in India circa 1800-1850. – J Asia Sep 6 '17 at 18:35
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The Muslim proportion in "undivided India" - today's India, Pakistan and Bangladesh - has risen from 21% in the late 19th century to about 31½% today, but there can be little doubt that the rate of increase was slower in the C19, much of the 20th-century growth being concentrated in the area now forming Pakistan which saw exceptional agricultural development from the 1880s. This is consistent with experience elsewhere: past populations were on the whole less mobile and less subject to rapid economic transformation than in recent times.

A tentative reconstruction for c.1850 based on McEvedy's breakdown into today's areas (Atlas of world population history, Penguin 1978) suggests about 11 million Muslims in what is now Pakistan, 23m in today's India and 15m in Bangladesh (against 15m, 29m and 19m respectively in 1901) - in all roughly a fifth. In 1800 with a total population of 190-200m we're probably looking at a Muslim contribution of 35-40 million (about a fifth of them in Pakistan, a half in India and 30% in Bangladesh) as there is no reason to assume any disproportionate advance in areas of predominantly Muslim settlement. It's certainly a good deal more than 25m or the first source's 13%, numbers derived from extending 20th-century trends into the 19th where they simply don't apply.

Of the three present-day states, Bangladesh has shown the least change in its share of the subcontinent's Muslim population, rising to 32% in the 1960s before falling back to 27% today: population movements at the time of partition raised Pakistan's share from under a quarter to more than a third while lowering India's from 45% to 35%: today Pakistan and India each contribute 36-37%.

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The graph in this answer to another question puts the population of the Indian subcontinent in 1800 at around 190 million. 13% of that would be 24.7 million, which corresponds very closely to your estimate of 24.05 million. So "25 million" is probably the right order of magnitude.

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