How this works
German income tax (Einkommensteuer) is computed from an official polynomial formula in § 32a EStG, not flat brackets. There are four zones: a tax-free zone up to the Grundfreibetrag (€11,604 in 2024), a steep progression zone from 14 % to 24 %, a shallower progression zone from 24 % to 42 %, and finally a flat 42 % up to €277,825 where the so-called Reichensteuer kicks in at 45 %. Married couples filing jointly use the Splittingtarif: tax is computed on half the joint income, then doubled — almost always cheaper than two single calculations when one spouse out-earns the other. The Solidaritätszuschlag (Soli) adds 5.5 % on top of the income tax, but a generous Freigrenze means roughly the bottom 90 % of earners no longer pay it (€18,130 of income tax for singles, €36,260 joint). Kirchensteuer (8 – 9 % of income tax, Land-dependent) isn't modelled because it only applies if you're a registered member of a tax-collecting church.
The formula
zvE = zu versteuerndes Einkommen (taxable income, after Werbungskosten and Sonderausgaben). The polynomial coefficients change yearly with the Grundfreibetrag — these are the 2024 values. Solidaritätszuschlag is 5.5 % of ESt with a Freigrenze of €18,130 (single) or €36,260 (joint); the Milderungszone tapers in at 11.9 % of excess. Excludes Sozialabgaben (Krankenversicherung, Rentenversicherung, etc., totalling roughly 20 % of gross), Werbungskostenpauschale (€1,230/year automatic), Kirchensteuer.
Example calculation
- Single filer, zvE €45,000, with Soli.
- In the (17,005 → 66,760) zone: z = (45,000 − 17,005)/10,000 = 2.7995. ESt = (181.19 × 2.7995 + 2,397) × 2.7995 + 1,025.38 ≈ €9,153.
- Soli: ESt < €18,130, so Freigrenze applies → €0. Total ≈ €9,153, effective rate ~20.3 %, Netto ≈ €35,847.
Frequently asked questions
Why does my Lohnsteuer on the payslip differ from this?
Lohnsteuer is the employer's monthly withholding estimate, not the final annual tax. It uses your Steuerklasse (I – VI), tax tables, and assumptions about a full year of equal monthly salary, which usually overshoot. The annual reconciliation in your Steuererklärung is what brings it to the figure this calculator estimates, then you get a refund (Erstattung) or pay a bit more (Nachzahlung).
When does Splittingtarif help married couples?
Whenever the spouses' incomes are unequal. Because the tax curve is progressive, calculating tax on the average and doubling is always ≤ taxing each individually. Two earners on €40k each see no benefit (the split halves to €40k anyway), but a €70k / €10k couple saves several thousand euros: instead of taxing €70k at the higher rates, both halves are taxed at the €40k Grundtarif level.
Do I owe Kirchensteuer? Why isn't it modelled?
Only if you're registered as a member of a Kirchensteuer-collecting denomination (mainly Catholic and Protestant) in Germany. The rate is 8 % of income tax in Bavaria and Baden-Württemberg, 9 % in the other Länder. Because it depends on personal religious-registration status which the calculator can't know, we leave it out — add 8 – 9 % of the displayed ESt to your tax if you're a tax-paying church member.