National Origins Formula foundational text Immigration Act of 1924
History
Temporary measures establishing quota limits per country based on the makeup of the foreign-born population residing in the U.S. were introduced in 1921 (Emergency Quota Act) and 1924 (Immigration Act of 1924); these were replaced by a permanent quota system based on each nationality's share of the total U.S. population as of 1920, which took effect on July 1, 1929 and governed American immigration law until December 1, 1965 (when the Immigration and Nationality Act of 1965 abolished it). The National Origins Formula aimed to preserve the existing ethnic proportions of the population as calculated according to data from the 1920 Census of Population.The 1921 Emergency Quota Act restricted immigration to 3% of foreign-born persons of each nationality that resided in the United States in 1910.
The Immigration Act of 1924, also called the National Origins Act, provided that for three years the formula would change from 3% to 2% and the basis for the calculation would be the census of 1890 instead of that of 1910. After June 30, 1927, total immigration from all countries will be limited to 150,000, with allocations by country based upon national origins of inhabitants according to the census of 1920. The quota system applied only to non-Asian immigrants. It aimed to reduce the overall number of unskilled immigrants, to allow families to re-unite, and to prevent immigration from changing the ethnic distribution of the population. The 1924 Act also included the Asian Exclusion Act, which limited immigration to persons eligible for naturalization. 
As a result, East Asians and South Asians were effectively banned from immigrating. Africans were also subjected to severe restrictions. Immigration from North and South America was not restricted.Quota calculation formula
The national origins formula prescribed by the Immigration Act of 1924, effective 1929, capped total annual quota immigration from outside the Western Hemisphere at 150,000. The quota for each country was to be computed as a fraction of 150,000 in a ratio proportional to the number of U.S. inhabitants of each national origin as a share of total inhabitants in 1920, with a minimum quota of 100. Due to the minimum rounding up the quotas for all countries that would not have otherwise reached 100, in practice the annual global quota total was slightly more than 150,000 (in 1930 totaling 153,714), but the formula calculation still used the fixed number 150,000.
The total number of U.S. inhabitants in 1920 with national origins in quota countries was 89,506,558 so the national origins formula f expressed mathematically as f = n/89,506,558 = q/150,000, where n is the number of inhabitants of any given national origin and q is the quota, hence to convert n into q required multiplication of n by  150,000/89,506,558 = 0.001675854857.
For example, the number of U.S. inhabitants in 1920 who were derived from the United Kingdom was fixed at 39,216,333 so the formula f = 39,216,333/89,506,558 = q/150,000. The formula could thus be solved for q as:
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