Percentage Calculator: The Three Questions and How to Answer Each

Percentages show up everywhere: discounts, tax, tips, grade changes, poll results, pay raises. Most people can do simple percentage math in their head, but the three distinct types of percentage questions require different formulas.

The Three Questions

Question 1: What is X% of Y?

"What is 15% of $83?"

Formula: (X/100) × Y = (15/100) × 83 = $12.45

Question 2: X is what percent of Y?

"28 is what percent of 200?"

Formula: (X/Y) × 100 = (28/200) × 100 = 14%

Question 3: What is the percentage change from X to Y?

"A stock went from $45 to $67. What's the percentage gain?"

Formula: ((Y - X)/X) × 100 = ((67-45)/45) × 100 = 48.9%

The Confusion Point

Questions 1 and 3 both produce a percentage, but from different inputs. Question 3 is the one most commonly botched:

"My salary went from $60,000 to $75,000 — that's a 25% raise."

Correct: (75,000 - 60,000) / 60,000 × 100 = 25% ✓

"The price dropped from $200 to $150 — that's a 50-dollar drop. 50/200 = 25% off."

Correct: (200 - 150) / 200 × 100 = 25% ✓

"A 20% discount on a $200 item saves $40. If the item goes back to $200 from $160, is that a 20% increase?"

No: (200 - 160) / 160 × 100 = 25% increase. Percentages are asymmetric — a 20% decrease requires a 25% increase to recover.

The Asymmetry of Percentage Changes

A 50% drop requires a 100% gain to recover. A 20% drop requires a 25% gain. This asymmetry is why investment losses are psychologically harder to recover from — mathematically they actually are harder.

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