Percentage Increase and Decrease: Examples That Stick

Most people learn the formula once in school and never touch it again — until life forces them to. Percentage change shows up everywhere — sales, salary raises, exam scores. Get the direction wrong and you misread the news.

The formula

% change = (new − old) / old × 100. Positive = increase. Negative = decrease.

Worked examples

$50 → $65 = +30%. $80 → $60 = −25%. Price doubles: +100%. Price halves: −50%.

The asymmetry trap

A 50% drop needs a 100% rise to recover. A stock down 80% must rise 400% to break even.

Percentage points vs percent

Interest rate going 4% → 5% is a 1 percentage point rise, but a 25% relative increase. Headlines often blur this.

Pro tips

• Always state the base. '20% increase' means nothing without knowing 20% of what.
• For compounding sequences, multiply the factors: +10% then −10% = 0.9 × 1.1 = 0.99, a small net loss.

Frequently asked questions

Why do losses hurt more than gains help? Asymmetry — a 30% loss requires a 43% gain to get back to flat.

What is reverse percentage? Finding the original number given the result and percentage change. $120 after a 20% markup → original = 120 / 1.20 = $100.

Run your own numbers before you trust a rule of thumb. Two minutes saves a lot of regret.