How do tax brackets actually work?

The US federal income tax is progressive and marginal, meaning income is sliced into bands and each band is taxed at its own rate. If the bracket boundary sits at $50,000 and you earn $52,000, only the $2,000 above the threshold is taxed at the higher rate; everything below is taxed at the lower rates, exactly as before. This is why your effective tax rate, total tax divided by total income, is always lower than your top marginal rate, often substantially. The widespread belief that a raise can push you into a bracket that leaves you worse off is simply false as a matter of bracket arithmetic.

Two honest caveats keep this from being absolute. Benefit cliffs are real: some income-tested programs, subsidies, and credits phase out or cut off at specific income levels, and crossing one of those can genuinely reduce net resources, which is a policy design problem rather than a feature of tax brackets. And the tax code contains many other moving parts, deductions, credits, payroll taxes with their own thresholds, capital gains taxed on separate schedules, and state taxes with their own structures, so effective rates vary widely across people with the same gross income. But the core mechanic is worth internalizing, because the misunderstanding leads people to turn down raises, overtime, and promotions on reasoning that does not hold.