Whether it's a 30% off sale, a 15% tip, or a 7% tax, percentages are part of daily life. Yet many people find them confusing. The good news: there are really only three types of percentage problems, and once you learn them, everything else is just application.
The Three Basic Percentage Problems
1. What is X% of Y?
The most common question. "What is 20% of 80?"
Formula: (X/100) × Y = Answer
Example: 20% of 80 = (20/100) × 80 = 0.2 × 80 = 16
Real life: A $80 shirt is 20% off. How much is the discount? $16.
2. X is what percent of Y?
"15 is what percent of 60?"
Formula: (X/Y) × 100 = Percentage
Example: (15/60) × 100 = 0.25 × 100 = 25%
Real life: You got 15 questions right out of 60. That's 25%.
3. X is Y% of what?
"30 is 20% of what number?"
Formula: X ÷ (Y/100) = Answer
Example: 30 ÷ (20/100) = 30 ÷ 0.2 = 150
Real life: You saved $30 on a 20% discount. The original price was $150.
Percentage Increase and Decrease
Calculating Increase
To find percentage increase: ((New - Old) / Old) × 100
Example: Price went from $50 to $65. Increase = ((65-50)/50) × 100 = 30%
Calculating Decrease
Same formula: ((Old - New) / Old) × 100
Example: Price dropped from $80 to $60. Decrease = ((80-60)/80) × 100 = 25%
Mental Math Shortcuts
- 10%: Move the decimal one place left. 10% of 250 = 25
- 5%: Find 10%, then halve it. 5% of 250 = 12.5
- 15%: 10% + 5%. 15% of 250 = 25 + 12.5 = 37.5
- 20%: 10% × 2. 20% of 250 = 50
- 25%: Divide by 4. 25% of 250 = 62.5
- 50%: Divide by 2. 50% of 250 = 125
Common Percentage Traps
Successive Percentages Don't Add
A 20% increase followed by a 20% decrease doesn't return you to the original. Start with 100: +20% = 120, then -20% of 120 = 96. You lost 4%.
Percentage Points vs. Percentage
"Interest rate rose from 2% to 3%" is a 1 percentage point increase but a 50% increase in rate.
The "Of" Problem
50% of 20 ≠ 20% of 50... wait, actually they ARE equal (both = 10). But 50% of 30 (15) ≠ 30% of 50 (15)... they're equal too! Fun fact: X% of Y always equals Y% of X.
Calculate Any Percentage
Quick percentage calculator for all three types of problems.
Open Percentage Calculator →Percentages in Finance
- Tax rate: Applied to income above thresholds (marginal)
- Interest rate: Usually annual (APR), sometimes compounded
- Investment returns: Often quoted before inflation
- Discounts: Always calculated on original price, not sale price
Mastering percentages is one of the most practical math skills you can develop. It shows up in shopping, cooking, finance, statistics, and countless other areas. Practice with real examples, and soon the calculations will become second nature.