Here is a table of definitions from the California DEPARTMENT OF HOUSING AND COMMUNITY DEVELOPMENT
Here are definitions from the HUD website:
Low Income
A household whose income does not exceed 80 percent of the median income for the area, as determined by HUD, with adjustments for smaller or larger families. HUD may establish income ceilings higher or lower than 80 percent of the median for the area median on the basis of HUD’s findings that such variations are necessary because of prevailing levels of construction costs or fair market rents, or unusually high or low family incomes.
Very Low-Income
Households whose incomes do not exceed 50 percent of the median area income for the area, as determined by HUD, with adjust-ments for smaller and larger families and for areas with unusually high or low incomes or where needed because of facility, college, or other training facility; prevailing levels of construction costs; or fair market rents.
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