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Of course, there are many other factors than just the total income that will come into play to affect how much tax will be paid. Deductions and credits can significantly reduce the tax that would be due. Individuals can give up to 50% of income to most charities and cut their taxable income up to half with that deduction alone.
Also, there are types of income that are not taxed or may be taxed at a lower rate.
Income from bonds issued to state and local governments is not subject to federal income tax so one could possibly have one million of that type of tax exempt income.
Gains on sale of investments and qualified dividends currently have a 15% tax rate so that would only be about 150,000 tax if all the one million was that type of income.
If the million was all wages or other ordinary income, such as a lottery, then a single person with no deductions would have taxable income of about $990,250 and tax in 2012 of about $323,350.
Depending on the circumstances the amount of tax on one million will vary with the type of income. It is such planning to have exempt or lower rate income that allows some millionaires from having to pay the possible maximum of about 33% on the million.
Please ask if you need clarification or more discussion.
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The 990,250 is after the standard deduction and exemption for a single person so that is the taxable income (with no other deductions like charity, mortgage interest, property tax. investment expenses, etc).
The tax on that 1,000,000 gross income with only the bare minimum deduction to have taxable income of 990,250 is 323,350.
The amount after tax would be 1,000,000 - 323,350 = 676,650.
That is sort of the worst case or most tax with no planning, no income at better rates, no deductions and no credits.
Let me know if you need more help.