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. Statutory 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. Average 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. Let be the total tax liability. Let be the total tax base. 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. Marginal A marginal tax rate is the tax rate on income set at a higher rate for incomes above a designated higher bracket, which in 2016 in the United States was $415,050. For annual income that was above the cut-off point in that higher bracket, the marginal tax rate in 2016 was 39.6%. For income below the $415,050 cut off, the lower tax rate was 35% 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.