# Tax rate

In a tax system, the tax rate is the ratio (usually expressed as a percentage) at which a business or person is taxed. There are several methods used to present a tax rate: statutory, average, marginal, and effective. These rates can also be presented using different definitions applied to a tax base: inclusive and exclusive.

A statutory tax rate is the legally imposed rate. An income tax could have multiple statutory rates for different income levels, where a sales tax may have a flat statutory rate.

The statutory tax rate is expressed as a percentage and will always be higher than the effective tax rate.

An average tax rate is the ratio of the total amount of taxes paid to the total tax base (taxable income or spending), expressed as a percentage.

In a proportional tax, the tax rate is fixed and the average tax rate equals this tax rate. In case of tax brackets, commonly used for progressive taxes, the average tax rate increases as taxable income increases through tax brackets, asymptoting to the top tax rate. For example, consider a system with three tax brackets, 10%, 20%, and 30%, where the 10% rate applies to income from \$1 to \$10,000, the 20% rate applies to income from \$10,001 to \$20,000, and the 30% rate applies to all income above \$20,000. Under this system, someone earning \$25,000 would pay \$1,000 for the first \$10,000 of income (10%); \$2,000 for the second \$10,000 of income (20%); and \$1,500 for the last \$5,000 of income (30%). In total, they would pay \$4,500, or an 18% average tax rate.

A marginal tax rate is the tax rate an individual would pay on one additional dollar of income. Thus, the marginal tax rate is the tax percentage on the last dollar earned. In the United States in 2013, for example, the highest marginal federal income tax rate was 39.6%, applying to earnings over \$400,000. Earnings under \$400,000 that year had a lower tax rate of 33% or less.

The marginal tax rate on income can be expressed mathematically as follows:

where t is the total tax liability and i is total income, and ∆ refers to a numerical change. In accounting practice, the tax numerator in the above equation usually includes taxes at federal, state, provincial, and municipal levels. Marginal tax rates are applied to income in countries with progressive taxation schemes, with incremental increases in income taxed in progressively higher tax brackets.

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