What is a percentage?
The word percentage comes from the Latin per centum, meaning “per hundred”. It is a way of expressing a proportion relative to 100, using the symbol %.
25% = 25/100 = 0.25 50% = 50/100 = 0.50 100% = the whole 150% = more than the whole
The 5 types of percentage calculation
- X% of Y: Value = (X ÷ 100) × Y
- X is what % of Y?: Percentage = (X ÷ Y) × 100
- Increase of X%: Final = Base × (1 + X/100)
- Discount of X%: Final = Base × (1 − X/100)
- Change %: Change = ((Final − Initial) ÷ |Initial|) × 100
Mental math tips
10%: divide by 10. 5%: half of 10%. 1%: divide by 100. 25%: divide by 4. 50%: divide by 2.
Combine these bases: 15% = 10% + 5%; 30% = 3 × 10%; 75% = 50% + 25%.
Compound percentages: be careful!
Two successive increases of 10% are not equal to 20%. Let us see:
Initial value: 100 After +10%: 100 × 1.10 = 110 After another +10%: 110 × 1.10 = 121 Total: a 21% increase, not 20%
Frequently asked questions
Can a percentage be greater than 100%?
Yes! If a company grew 150%, it more than doubled. 200% = tripled. Percentages above 100 are common in growth changes.
How do you find the original value after a discount?
If a product costs $80 after a 20% discount, the original is: 80 ÷ (1 − 0.20) = 80 ÷ 0.80 = $100.
What is the difference between a percentage point and a percent?
If a rate rises from 10% to 12%, the increase is 2 percentage points (pp), but 20% in relative terms. Confusing the two is a common mistake in economic news.
How do you calculate interest with percentages?
Simple interest: I = Principal × rate × time. Compound interest: A = Principal × (1 + rate)^time. The percentage is applied as a factor (0.01 per 1%).