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The largest standard deduction for a dependent is the greater of $850 or total wages plus $300, but in no case can the standard deduction be more than $5,350. Any income in excess of these amount is taxable.
Someone claimed as a dependent will pay tax on a return if any of the following apply.
1. Unearned income (which includes taxable interest, ordinary dividends, and capital gain distributions) was more than $850.
2. Earned income (which includes wages, tips, and taxable scholarship and fellowship grants) was more than $5,350.
3. Gross income (which is the total of your unearned and earned income was more than the larger of
a. $850, or
b. their earned income (up to $5,050) plus $300.
For dependents the type of income as well as the amount is a factor in how much income they can have before paying tax.
If there is no unearned income (dividends, interest, etc) then they can earn $5,350 before they have to pay any tax.
But, if there is unearned income that is more than $850 there will be some tax due even if they have no other earnings.
I hope this is the information you need for the amount a dependent can earn before it is taxable.