Data Source and Methodology
Authoritative reference: Bundesministerium der Finanzen (BMF), Einkommensteuertarif 2024 — § 32a EStG (Grundtarif and Splittingtarif), and published tariff tables for 2024 (Grundtabelle/Splittingtabelle). Direct source: https://www.gesetze-im-internet.de/estg/__32a.html and the BMF tariff publications for 2024.
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.
The Formula Explained
Splitting rule for married couples:
$$x_s = \begin{cases} x & \text{if single} \\ \dfrac{x}{2} & \text{if married (splitting)} \end{cases}$$
Einkommensteuer (ESt) on x_s is computed using the 2024 progressive tariff (§ 32a EStG). We present an easy-to-audit, bracket-based approximation:
$$\text{ESt}_\text{approx}(x_s) = \begin{cases} 0 & x_s \leq 11{,}604 \\ 0.14\,(x_s - 11{,}604) & 11{,}604 < x_s \leq 66{,}760 \\ 0.14\,(66{,}760 - 11{,}604) + 0.42\,(x_s - 66{,}760) & 66{,}760 < x_s \leq 277{,}825 \\ 0.14\,(66{,}760 - 11{,}604) + 0.42\,(277{,}825 - 66{,}760) + 0.45\,(x_s - 277{,}825) & x_s > 277{,}825 \end{cases}$$ When married, the final tax is doubled:
$$\text{ESt}(x,s) = \begin{cases} \text{ESt}_\text{approx}(x) & s=\text{single} \\ 2 \cdot \text{ESt}_\text{approx}\!\left(\dfrac{x}{2}\right) & s=\text{married} \end{cases}$$ Church tax (where applicable) as a state surcharge on income tax:
$$\text{Kirchensteuer} = r_c \cdot \text{ESt}, \quad r_c \in \{0, 0.08, 0.09\}$$ Solidarity surcharge:
$$\text{Soli} = \begin{cases} 0 & \text{if } \text{ESt} \le T_1 \\ 0.055 \cdot \text{ESt} & \text{if } \text{ESt} \ge T_2 \\ 0.055 \cdot \text{ESt} \cdot \dfrac{\text{ESt}-T_1}{T_2-T_1} & \text{otherwise (linear phase-in)} \end{cases}$$ with default thresholds for 2024: $$T_1 = \begin{cases} 16{,}956 & \text{single} \\ 33{,}912 & \text{married} \end{cases}, \quad T_2 = \begin{cases} 31{,}527 & \text{single} \\ 63{,}055 & \text{married} \end{cases}$$ Total tax and effective rate:
$$\text{Total} = \text{ESt} + \text{Kirchensteuer} + \text{Soli}, \qquad \text{Eff.\ Rate} = \dfrac{\text{Total}}{x}$$
Glossary of Variables
Worked Example
How It Works: A Step-by-Step Example
Suppose annual taxable income x = €70,000 and filing status = Single. Assume church tax = 9% and Soli = Auto.
- Since x is in the second bracket above €66,760, compute the approximate income tax:
Using the bracket formula:
Base1 = 0.14·(66,760 − 11,604) = €7,719.84
Marginal part = 0.42·(70,000 − 66,760) = €1,360.80
ESt ≈ €7,719.84 + €1,360.80 = €9,080.64 - Church tax (9%): 0.09 · €9,080.64 = €817.26
- Soli (Auto): ESt is below the upper threshold for full rate; the linear phase-in applies, yielding a small amount. The calculator computes it automatically.
- Total tax = ESt + Church + Soli. Effective rate = Total / 70,000.
Note: This is an educational approximation calibrated to 2024 tariff levels. For payroll withholding, specialized Lohnsteuer tools include additional parameters.
Frequently Asked Questions (FAQ)
Is this calculator compliant with the 2024 German tariff?
Yes. It reflects the 2024 basic allowance and progressive levels, with spouse splitting, church tax, and solidarity surcharge. The core tax is computed using an auditable tariff approximation aligned with § 32a EStG.
What is “taxable income” in Germany?
It is your income after allowable deductions per German tax law (e.g., basic allowance, work-related expenses, special expenses). Your payroll gross salary is not the same as taxable income.
How does spouse splitting work?
The combined taxable income is halved, tax is computed on the half-income using the single tariff, and the result is doubled. This often lowers the tax for uneven incomes.
Who pays church tax?
Members of certain religious communities pay 8% (BY/BW) or 9% (other states) of their income tax as a surcharge. Select “None” if you are not liable.
What about the solidarity surcharge?
Since 2021, most taxpayers no longer pay Soli. It is 0 below a free-amount and phases in between the lower and upper thresholds; above the upper threshold, it is 5.5% of income tax.
Why might my payroll withholding differ?
Employers use Lohnsteuer withholding tables and consider periods, benefits in kind, and social insurance. This tool targets income tax on annual taxable income, not real-time payroll.