Progressive tax

A  takes a larger percentage of income from high-income groups than from low-income groups and is based on the concept of ability to pay. A progressive tax system might, for example, tax low-income taxpayers at 10 percent, middle-income taxpayers at 15 percent and high-income taxpayers at 30 percent. The U.S. federal income tax is based on the progressive tax system.

Tax rate increases as Taxable income increases
Before looking at how this works in the U.S. income tax system, the concept of "Taxable income" needs to be understood. The IRS defines "Taxable income" (upper case "T") on the Form 1040 different than "taxable income" (lower case "t").

In particular, "Taxable income" is one's Adjusted Gross Income (AGI) reduced by one's Standard (or Itemized) Deductions. (The value of the deductions is not taxed.) This meaning refers to the similarly named line on Form 1040.

The other term, "taxable income" (lower case "t"), is used in contrast to "nontaxable income".

This table shows how to calculate taxes to be paid on Taxable income by a single person in 2018.

As Taxable income increases, the amount of tax paid on each additional dollar increases (see Marginal rate below). This is the progressive aspect of the tax - higher income means possibly paying more tax on that additional portion of income. A proportional tax would pay the same percentage regardless of income.

The figure below is a graphical representation of the tax table.

Tax bracket
A tax bracket is the range of Taxable income to which a tax rate applies. In this example, there are seven ranges of Taxable income. Each range is taxed at a different rate and is therefore a separate tax bracket. The tax brackets in the above table are 10%, 12%, 22%, 24%, 32%, 35%, and 37%. (The tax bracket column is not present in the actual IRS table. It was added here to show the concept.)

Marginal rate
Within each tax bracket, each additional dollar will impose the same amount of tax. For example, you will pay a tax of 10% if your income is $5,000 ($500 tax) or $9,000 ($900 tax).

If your Taxable income increases to $10,000, your next dollar of Taxable income is taxed at a 12% rate. This is a higher marginal rate than the 10% rate imposed for $9,000.

The marginal rate is not the total tax you pay. It only describes the rate of the tax paid for that specific amount of Taxable income.

Calculation of the income tax
The actual IRS instructions require use of the tax tables which provide the tax directly from your income. No calculations are required. The following example is for illustrative purposes to show how the tax schedules work.

A single person has a Taxable income of $60,000 which falls within the 22% tax bracket.

The approach is to add the amount of each underlying tax bracket up to the total Taxable income and is shown graphically in the figure below.

For convenience, the IRS places the sum of the underlying tax brackets in the same row as the Taxable income. The amount of $4,453.50 is the sum of the 10% and 12% brackets ($3,501.00 + $952.50).

$$ \begin{align} \text{Total tax} & = $4,453.50 + 22% * ($60,000 - $38,700) \\ & = $9,139.50 \end{align} $$

The manual calculation and IRS table results are identical ($9,139.50).

A misconception about progressive tax
A common misconception is that changing your tax bracket implies that your entire income is taxed at that rate.

As demonstrated in the previous example, you are only taxed at the marginal rate for the amount of income which applies to that tax bracket.

This is much lower than incorrectly calculating a tax of $13,200 (22% * $60,000) on the entire income at the 22% marginal rate.