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The tax rate indicates what percent of the assessment basis or what absolute amount of money per unit of the assessment basis is levied as taxes by the fiscal authorities. The term tax scale is used if the tax rate is not constant for the entire assessment basis. Thus, a tax scale consists of a sequence of tax rates.

Tax scales can be simple tax scales (dependent on only one variable, e.g. the personal income tax scale, which is only dependent on the amount of taxable income) or combined scales (dependent on more than one variable, e.g. the inheritance tax scale, which is dependent on the amount of the inheritance as well as the degree of relationship). The scales of personal taxes are usually constructed progressively, i.e. the tax rate and the resulting average tax burden increase with the assessment basis.

The basic tax rate is the tax rate that must be paid for the first Euro of the taxpayer’s assessment basis.

On the other hand, the top tax rate is the highest tax rate provided for in a tax scale (= maximum marginal tax rate).

The average tax rate results from the amount of taxes to be paid divided by the respective assessment basis. If the tax rate is expressed as a percentage, the result is to be multiplied by a factor of 100.

The marginal tax rate or the marginal rate of tax is the tax rate at which the last (highest) unit of the assessment basis achieved is taxed. The marginal tax rate results from the first derivative of the tax function.

The differential tax rate is the average tax rate levied on an additional part of the assessment basis (B_z). If the taxes on the assessment basis including B_z are depicted as S_z and as S for the taxes without this part of the assessment basis, the differential tax rate is calculated as (S_z – S)/B_z.

The scale can be designed as a calculation scale or as a threshold scale (graduated scale). In the calculation scale, the rate that applies to the last unit of taxation shall apply to the entire assessment basis. In the case of the threshold scale or graduated scale, the assessment basis is broken down into portions, to which a certain tax rate is then applied respectively. The personal income tax scale in Germany is designed as a threshold scale. In 2018 the following scale applies:

•From € 0 to € 9,000:	Basis tax allowance; not subject to taxation (cf. Sec. 32a (1) sent. 2 no. 1 EStG)
•From € 9,001 to € 13,996:	Transition to linear-progressive development. The marginal tax rate increases from a basic tax rate of 14 % to 23.87 % (cf. Sec. 32a (1) sent. 2 no. 2 EStG).
•From € 13,997 to € 54,949:	Linear-progressive development with a quick increase in the marginal tax rate up to 42 % (cf. Sec. 32a (1) sent. 2 no. 3 EStG).
•From € 54,950 to € 260,532:	Proportional development with a marginal tax rate of 42 % (cf. Sec. 32a (1) sent. 2 no. 4EStG).
•Above € 260,533:	Proportional development with a top tax rate of 45 % (cf. Sec. 32a (1) sent. 2 no. 5 EStG), so-called wealth tax (Reichensteuer).

Figure 6: Tax scale in 2018