Prozentrechner (Percentage Calculator)

Every percentage calculation links three quantities. If you know two of them, you can find the third.

• Base value (Grundwert, G): the starting or total amount that equals 100 % (e.g. 200 €).
• Percentage rate (Prozentsatz, p): the share expressed in percent (e.g. 25 %).
• Percentage value (Prozentwert, W): the actual amount that corresponds to the rate (e.g. 50 €).

Rule of thumb: the rate is the number with the % sign; the value is an amount in the same unit as the base (euros, kilograms, pieces).

These three quantities give three base formulas:

All three derive from the same core equation W ÷ G = p ÷ 100 – you simply rearrange it for the unknown quantity.

Most percentage tasks ask for the percentage value: „How much is p % of G?" You multiply the base value by the rate and divide by 100.

W = G × p ÷ 100

Discount: 20 % off 79.99 €

• Discount ≈ 16.00 € (exactly 15.998 €) = 79.99 € × 20 ÷ 100
• New price = 79.99 € × 0.80 = 63.99 €

Tip: 10 % on 42.00 €

• Tip = 42.00 € × 10 ÷ 100 = 4.20 €
• Total = 42.00 € + 4.20 € = 46.20 €

VAT (MwSt): 19 % on 100.00 € net

• VAT = 100.00 € × 19 ÷ 100 = 19.00 €
• Gross price = 100.00 € + 19.00 € = 119.00 €

For both tax rates and more examples, see the VAT calculator and the article 7 % or 19 % VAT.

Salary raise: 5 % on 3,200.00 €

• Raise = 3,200.00 € × 5 ÷ 100 = 160.00 €
• New salary = 3,200.00 € + 160.00 € = 3,360.00 €

In every case the rule is the same: first calculate the percentage value, then add it to the base (surcharge) or subtract it (discount).

Percentage change shows by how many percent a value has risen or fallen against a starting value. The reference is always the old value (= 100 %).

Change in % = (new value − old value) ÷ old value × 100

Increase example: from 100 to 119

• (119 − 100) ÷ 100 × 100 = 19 ÷ 100 × 100 = +19 %

Decrease example: price from 80.00 € to 60.00 €

• (60.00 − 80.00) ÷ 80.00 × 100 = −20.00 ÷ 80.00 × 100 = −25 %

A negative result means a decrease, a positive one an increase. Important: the reference value matters. If a value rises by 50 % and then falls by 50 %, you do not return to the start – 100 becomes 150, then 75, because the second calculation refers to 150.

The Dreisatz (rule of three) is the most intuitive way to calculate percentages – without any formula. You reason from the whole (100 %) via one unit (1 %) to the share you want.

Example: How much is 23 % of 250 €?

1. 100 % equals 250 € – this is the base value.
2. 1 % equals 250 € ÷ 100 = 2.50 € – you divide by 100.
3. 23 % equals 2.50 € × 23 = 57.50 € – you multiply by the rate.

The beauty of the Dreisatz: it works both ways. To find the rate instead („57.50 € is what percent of 250 €?"), go via 1 €: 250 € = 100 %, so 1 € = 0.4 %, and since 1 € = 0.4 %, 57.50 € equals 57.50 × 0.4 = 23 %. Just as quickly: 57.50 € ÷ 2.50 € = 23, so 23 %.

The Dreisatz is especially handy with „awkward" rates, because the intermediate „1 %" step reduces every task to a simple multiplication.

Percent is just another notation for a fraction with denominator 100. To convert percent into a decimal, divide by 100 (move the decimal point two places left). To go back, multiply the decimal by 100.

Decimal = percent ÷ 100

In practice the decimal form is fastest: 19 % of 100 € is 0.19 × 100 € = 19 €. Spreadsheets work exactly the same way when you multiply a cell by *0.19.

Percent and percentage points are often confused, even though they measure different things. The distinction only matters when the starting value is itself already a percentage (e.g. an interest rate, a quota, or an election result).

• Percentage points are the absolute difference between two percentages.
• Percent measures the relative change of that number.

Example: an interest rate rises from 10 % to 12 %.

• That is an increase of 2 percentage points (12 − 10).
• It is also an increase of 20 percent, since (12 − 10) ÷ 10 × 100 = 20 %.

Both statements are correct – they just answer different questions. „By how many percentage points?" asks for the absolute difference, „by how many percent?" for the relative change. In news about interest rates, inflation or elections, this distinction is decisive for a correct reading.

Three mistakes lead to wrong results particularly often:

1. Discounts and surcharges do not cancel out. A price first raised by 20 % and then cut by 20 % does not return to the start: 100 € → 120 € → 96 €. The reason: the second percentage refers to the already changed value.

2. Never subtract VAT from the gross price. To extract 19 % VAT from a gross price, do not multiply by 0.81 – divide by 1.19. 119.00 € gross becomes 119.00 € ÷ 1.19 = 100.00 € net, not 119.00 € × 0.81 = 96.39 €. The 19 % refers to the net amount, not the gross. The correct formula and a ready-made tool are at extract VAT.

3. Wrong reference value for the rate. For „X is what percent of Y?" you must always divide by Y (the base, 100 %), not by X. 30 of 120 is 30 ÷ 120 × 100 = 25 %, not 120 ÷ 30.

VAT (Mehrwertsteuer) is the most common percentage calculation in Germany. Every invoice, every receipt, and every VAT return is built on the 19 % or 7 % rate. Anyone self-employed converts gross to net and back every day.

• Adding VAT: gross = net × 1.19 (at 19 %)
• Extracting VAT: net = gross ÷ 1.19

The VAT calculator and the Umsatzsteuer-Rechner handle both operations in seconds – including the 7 % rate and a full gross-net breakdown via the gross-net calculator.

Discount (Rabatt) and Skonto (an early-payment discount, e.g. „2 % if paid within 10 days") are also pure percentage math. Skonto is deducted from the gross invoice amount. If you want to show a discount or Skonto directly on an invoice, create a § 14 UStG-compliant invoice with the invoice generator – or, as a small business (Kleinunternehmer), without VAT.

In spreadsheets you calculate percentages with a simple multiplication. The % sign is a real operator there: 19% internally stands for the value 0.19.

• Percentage value: =A1*19% or equivalently =A1*0.19 – calculates 19 % of cell A1.
• Percentage rate: =A1/B1, then format the cell as percent – gives what percent A1 is of B1.
• Surcharge: =A1*1.19 – adds 19 % onto A1 (e.g. VAT).
• Reduction: =A1*0.8 – takes 20 % off A1.
• Percentage change: =(B1-A1)/A1 – change from A1 (old) to B1 (new).

Important: apply the „percent format" to the result cell only when the result is a rate. For euro amounts, keep the number format on currency – otherwise the sheet shows 1.900 % instead of 19,00 €.