Percentages appear in discounts, interest, tax and statistics. Three basic formulas cover most everyday calculations. This guide explains each one with a simple example.
Three key terms
- Base value (G): the whole amount, equal to 100%.
- Percentage rate (p): the rate expressed as a percentage.
- Percentage value (P): the portion of the base value.
1. Calculate the percentage value
Formula: P = G × p ÷ 100
Example: What is 15% of €200? €200 × 15 ÷ 100 = €30.
2. Calculate the percentage rate
Formula: p = P ÷ G × 100
Example: €30 is what percentage of €200? €30 ÷ €200 × 100 = 15%.
3. Calculate the base value
Formula: G = P ÷ p × 100
Example: €30 is 15% of what amount? €30 ÷ 15 × 100 = €200.
Calculate a percentage change
Divide the difference by the starting value, then multiply by 100:
- From €80 to €100: (€100 − €80) ÷ €80 × 100 = +25%.
- From €100 back to €80: (€80 − €100) ÷ €100 × 100 = −20%.
This shows why a 25% rise followed by a 25% fall does not return to the starting price: each change uses a different base.
Percentages and percentage points
If an interest rate rises from 2% to 3%, that is an increase of one percentage point, or 50% relative to the original rate. The two terms are often confused.
Everyday examples
| Situation | Calculation |
|---|---|
| €80 jacket with a 25% discount | €80 × 0.75 = €60 |
| Price including 19% VAT | Net × 1.19 |
| 10% tip on a €45 bill | €45 × 0.10 = €4.50 |
Try your own values with the percentage calculator or discount calculator.