Calculating Percentages: Formulas, Examples, Common Mistakes
Base value, percentage and percentage value explained: the three formulas with examples, percentage change, percentage points and removing VAT correctly.
Math & Technology3 linked calculatorsReading time: 6 min.
Per cent means “per hundred”. Keep three terms apart and you can solve any percentage problem – from a discount in a shop to a pay rise or the VAT on an invoice.
Key takeaways
- Every percentage problem has three quantities: the base value (the whole), the rate and the percentage value (the part).
- Percentage value = base value × rate ÷ 100 – the other two formulas are rearrangements of it.
- A percentage change always refers to the starting value.
- If an interest rate rises from 2 to 3 percent, that is 1 percentage point, but 50 percent more.
- Net from gross in Germany: divide by 1.19, do not subtract 19 percent.
Base value, rate, percentage value
One percent is one hundredth: 1% = 1/100 = 0.01. Every percentage calculation links three quantities:
- Base value (B) – the whole you start from, i.e. 100 percent: the old price, the salary, the total count.
- Rate (p) – the share in percent, for example 19% or 25%.
- Percentage value (V) – the share in the same unit as the base value, for example €47.50 or 36 items.
The three formulas
| Wanted | Formula | Example |
|---|---|---|
| Percentage value V | V = B × p ÷ 100 | 19% of €250.00 = €47.50 |
| Rate p | p = V ÷ B × 100 | 36 of 48 = 75% |
| Base value B | B = V × 100 ÷ p | €12.00 is 8% of €150.00 |
Rule of three as a memory aid
If you forget the formulas, go via 1%: first divide by 100 (or by the known rate), then multiply by the rate you are looking for. That is the rule of three.
Calculate percentages instantly
Percentage value, rate, base value or change – enter two values and the third appears with the working.
Change and percentage points
The percentage change is (new value − old value) ÷ old value × 100. The old value is the base value.
Example, the German minimum wage: on 1 January 2027 it rises from €13.90 to €14.60 per hour. That is €0.70 more, an increase of 5.04%.
Percentage points are the distance between two percentages. If an interest rate rises from 2% to 3%, it has risen by 1 percentage point – but by 50 percent measured against the old rate.
Several discounts are not added up: first 20% and then another 10% off the reduced price add up to 28% off, not 30%.
Calculate discount and final price
Discount in percent or euros, including several discounts in a row.
Calculating VAT correctly
German VAT is 19% at the standard rate and 7% at the reduced rate of the taxable amount (Section 12 UStG). The taxable amount is the net price – here it is the base value.
Net to gross: net price × (1 + 19 ÷ 100), i.e. times 1.19.
Common mistake when removing VAT
Subtracting 19% from €119.00 gross gives €96.39 – wrong, because the 19% was calculated on the net price, not the gross price. Correct: €119.00 ÷ 1.19 = €100.00 net.
Calculate VAT
Net, gross and tax amount for both German VAT rates.
Frequently asked questions
How do I work out a percentage?
How do I add a percentage to an amount?
What is the difference between percent and percentage points?
Why don't a 50% loss followed by a 50% gain bring back the original amount?
Sources
Every figure in this article comes from these primary sources or from the linked calculators, which are based on the same sources.
- Section 12 UStG – VAT rates (accessed September 30, 2026)
- Section 1 MiLoV5 – statutory minimum wage (accessed September 30, 2026)
Full-Stack Developer & Founder of HEADON.pro
Full-stack developer and founder of HEADON.pro. Developer of Rechnerzentrale.