Percentages and shares (Prozentrechnung)
A percentage is a rate per hundred: 19% of an amount means 19 out of every 100 units of it. Prozentrechnung (percentage arithmetic) converts a share into a number you can compare across different contexts — tax rates, interest rates, contribution rates, price changes — regardless of the absolute sum involved.
Why it matters
Percent is the unit German personal finance runs on. Income tax brackets, Sozialversicherung (social insurance) contributions, VAT, savings account interest, ETF cost ratios, and salary raises are all expressed as percentages, not fixed euro amounts. Reading a Gehaltsabrechnung (payslip), a Steuerbescheid (tax assessment), or a fund factsheet means converting a percentage into a concrete euro number, and back again.
Two related but different ideas cause most confusion: a change measured "in percent" (relative to a starting value) versus a change measured "in percentage points" (an absolute difference between two percentages). Mixing them up produces numbers that are off by a wide margin, especially with tax rates and interest rates.
Worked examples
1. Percent of a base — VAT on a purchase. Germany's standard VAT (Umsatzsteuer, value-added tax) rate is 19% (2026) [1]. A laptop priced at €1,200 net carries 19% x €1,200 = €228 in VAT, for a gross price of €1,428. The calculation: multiply the base by the rate expressed as a decimal (19% = 0.19).
2. Percentage change — a raise or a rent increase. A salary moves from €3,000 to €3,300 per month. The percentage change is (€3,300 - €3,000) / €3,000 = 0.10 = 10%. The base for a percentage change is always the starting value, not the ending one — reversing a 10% increase does not mean subtracting 10% from the new figure (€3,300 x 0.90 = €2,970, not €3,000).
3. Percentage points versus percent — reading a rate change. Suppose a savings account's interest rate rises from 2% to 3%. That is an increase of 1 percentage point (3 minus 2), but a 50% increase in the rate itself (1 / 2 = 0.50). Tax-bracket and contribution-rate discussions often quote the percentage-point figure because it is the smaller, more sober number — mixing it up with "percent" overstates or understates the real change.
4. Share of a budget. A household spends €900 of a €3,000 net income on rent (Kaltmiete, cold rent excluding utilities). That share is €900 / €3,000 = 0.30 = 30% of net income — a single number that stays comparable even if the household's income or city changes.
Check yourself
A laptop costs €1,200 net. Germany's standard VAT (Umsatzsteuer) rate is 19% (2026). How much VAT, in euros, is added to the price?
A savings account's interest rate rises from 2% to 3%. By how many percentage points did the rate increase?
Using the same rate move — from 2% to 3% — by what percent did the rate increase relative to its starting value?
A monthly salary rises 10%, from €3,000 to €3,300. It later falls 10%. What is the resulting salary?
Sources
- Bundesministerium der Finanzen — Umsatzsteuer-Anwendungserlass, §12 UStG (standard VAT rate 19%), https://www.bundesfinanzministerium.de/Content/DE/Standardartikel/Themen/Steuern/Steuerarten/Umsatzsteuer/umsatzsteuer.html (2026)