Wie man prozentuale Zu- und Abnahme berechnet

Percentage increase and decrease are among the most practical math skills you can master. Whether you are comparing prices, tracking investment returns, or analyzing data trends, knowing how to calculate these values accurately is essential. This guide covers the formulas, walks through real-world examples, and highlights the most common mistakes people make.

The formula for percentage increase is: Percentage Increase = ((New Value − Old Value) / Old Value) × 100. A positive result confirms an increase. For example, if your monthly salary goes from $4,000 to $4,500, the percentage increase is ((4,500 − 4,000) / 4,000) × 100 = 12.5%. According to the U.S. Bureau of Labor Statistics, the average annual wage increase in the United States has hovered between 3% and 5% in recent years, making a 12.5% jump notably above average.

The formula for percentage decrease works the same way but produces a negative result: Percentage Decrease = ((New Value − Old Value) / Old Value) × 100. If a laptop's price drops from $1,200 to $900, the percentage decrease is ((900 − 1,200) / 1,200) × 100 = −25%. You can express this as a 25% decrease. This is the same percentage change formula explained in our article on percentage change formulas, just applied to a decreasing value.

One of the most common mistakes is using the wrong base value. The denominator in the formula must always be the original (old) value — the value you are measuring the change from. Switching the old and new values in the denominator produces an incorrect result. For instance, if a stock rises from $50 to $75, the correct increase is ((75 − 50) / 50) × 100 = 50%. If you mistakenly divide by the new value 75, you get only 33.3%, which is wrong.

Another frequent error involves confusing percentage points with percentage change. If an interest rate rises from 3% to 5%, that is a 2 percentage point increase. However, in percentage terms, it is a ((5 − 3) / 3) × 100 = 66.7% increase. As Khan Academy explains, percentage points describe the absolute difference between two percentages, while percentage change measures the relative shift from the original value.

Successive percentage changes are another area where intuition often fails. If a product's price increases by 20% and then decreases by 20%, many people assume the price returns to its original amount. It does not. Starting at $100, a 20% increase brings the price to $120. A 20% decrease from $120 is $24, making the new price $96 — a net loss of 4%. This happens because the base changes after the first adjustment. For a deeper exploration of how successive changes interact, see our guide to everyday percentage tips.

Percentage increase and decrease appear constantly in the real world. Inflation, reported monthly by the Bureau of Labor Statistics via the Consumer Price Index (CPI), is expressed as a year-over-year percentage change. If the CPI rises from 296 to 305 over 12 months, the inflation rate is ((305 − 296) / 296) × 100 ≈ 3.04%. Understanding this calculation helps you interpret economic news and plan your personal finances.

In retail, percentage decrease drives purchase decisions. A '40% off' sale means the new price is 60% of the original. On a $250 item, you pay $250 × 0.60 = $150, saving $100. Stacked discounts — say 20% off plus an extra 10% — do not add to 30%. Instead, you pay 80% of the price after the first discount, then 90% of that: $250 × 0.80 × 0.90 = $180, which is 28% off, not 30%. For more shopping calculation tricks, see our percentage discount calculator guide.

In health and fitness, percentage change tracks progress. If your body weight drops from 200 lbs to 185 lbs, the percentage decrease is ((185 − 200) / 200) × 100 = −7.5%, or a 7.5% loss. Trainers and nutritionists commonly use percentage-based goals because they normalize progress across different body types, according to the American Council on Exercise.

To convert a percentage increase or decrease back to a multiplier, divide by 100 and add 1 (for increase) or subtract from 1 (for decrease). A 15% increase corresponds to a multiplier of 1.15. A 15% decrease corresponds to 0.85. This multiplier form is useful for spreadsheet calculations and compound growth modeling.

Here is a quick reference table: - 10% increase → multiply by 1.10 - 25% increase → multiply by 1.25 - 50% increase → multiply by 1.50 - 10% decrease → multiply by 0.90 - 25% decrease → multiply by 0.75 - 50% decrease → multiply by 0.50

For compound changes over multiple periods, use the formula: Final Value = Original Value × (1 + r₁/100) × (1 + r₂/100) × ... where r₁, r₂, etc. are the individual percentage changes (negative for decreases). This correctly handles the compounding effect that makes successive percentage changes non-additive.

Mastering percentage increase and decrease gives you a powerful analytical tool. From evaluating salary offers to comparing year-over-year business metrics, this calculation underpins countless decisions. Use our free percentage calculator to verify your work instantly — just select the '% Change' mode, enter your old and new values, and read the result.