How to Calculate Percentages: Complete Guide with Examples
Percentages come up everywhere — sales tax, tips, discounts, test scores, statistics, and more. This guide covers every type of percentage calculation you'll encounter, with clear formulas and worked examples.
The Basic Percentage Formula
At its core, percentage means "per hundred." The fundamental formula:
Example: You scored 42 out of 50 on a test. What percentage is that?
Percentage = (42 ÷ 50) × 100 = 84%
Finding a Percentage OF a Number
Examples:
- What is 15% of $80? → (15 ÷ 100) × 80 = $12
- What is 7.5% tax on $120? → 0.075 × 120 = $9
- What is 30% off $250? → 0.30 × 250 = $75 off → $175 final price
Percentage Change (Increase & Decrease)
Positive result = increase. Negative result = decrease.
- Price went from $50 → $65: ((65–50) ÷ 50) × 100 = +30% increase
- Salary cut from $80K → $72K: ((72K–80K) ÷ 80K) × 100 = –10% decrease
Percentage Difference Between Two Numbers
Use this when there's no "original" and "new" — just two values to compare.
Example: Store A charges $90, Store B charges $110.
Average = (90+110)/2 = 100
% Difference = (|90–110| ÷ 100) × 100 = 20% difference
Reverse Percentage: Finding the Original Value
Example: A price after 20% increase is $120. What was the original?
Original = $120 ÷ 1.20 = $100
Example: Item costs $85 after 15% discount. Original price?
Original = $85 ÷ (1 – 0.15) = $85 ÷ 0.85 = $100
Mental Math Shortcuts
- 10%: Move decimal one place left ($340 → $34)
- 5%: Find 10% then halve it ($340 → $34 → $17)
- 15%: Find 10% + half of 10% ($340 → $34 + $17 = $51)
- 20%: Find 10% then double it ($340 → $34 × 2 = $68)
- 25%: Divide by 4 ($340 ÷ 4 = $85)
- 50%: Divide by 2 ($340 ÷ 2 = $170)