How to calculate a percentage (the 3 questions people actually ask)
"Percentage" covers three different everyday questions, and mixing them up is where the confusion starts. Here's each one with a formula you can actually remember.
1. What is X% of a number?
This is for discounts, tips, and taxes. Multiply the number by the percent, divided by 100.
20% of 150 = 150 × 20 ÷ 100 = 30. So a 20%-off on a $150 item saves you $30.
2. X is what percent of Y?
This is for scores and proportions. Divide the part by the whole, then multiply by 100.
45 out of 60 on a test = 45 ÷ 60 × 100 = 75%.
3. Percentage change (increase or decrease)
This is for growth, price changes, and before/after comparisons. Subtract old from new, divide by the old value, multiply by 100.
Price went from $80 to $100: (100 − 80) ÷ 80 × 100 = +25%. From $100 to $80: (80 − 100) ÷ 100 × 100 = −20%.
The mistake almost everyone makes
A 20% increase followed by a 20% decrease does not bring you back to where you started — because the second 20% is taken from a bigger number. $100 up 20% is $120; $120 down 20% is $96, not $100. Percentages are always relative to whatever base they're applied to.