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For example, if someone (single filer) makes 45k in regular income and wants to sell stock which would realize 5k of long-term capital gains:

Do they pay 15% on the capital gains because, with 50k total income, they are in the 15% capital gains bracket?

Or, do they pay 0% on the capital gains because, with 50k total income minus the 12k standard deduction (38k), they are in the 0% capital gains bracket?

This question is similarly about deductions and capital gains, but doesn't answer about when the bracket changes.

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From Tax Topic 409: (emphasis added)

The tax rate on most net capital gain is no higher than 15% for most taxpayers. Some or all net capital gain may be taxed at 0% if you're in the 10% or 12% ordinary income tax brackets. However, a 20% tax rate on net capital gain applies to the extent that a taxpayer's taxable income exceeds the thresholds set for the 37% ordinary tax rate ($425,800 for single; $479,000 for married filing jointly or qualifying widow(er); $452,400 for head of household, and $239,500 for married filing separately.

So the capital gain tax brackets are based on the taxable income brackets (meaning after all income and deductions, but before credits).

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