What Is a Percentage?
A percentage is a way to express a number as a fraction of 100. The word “percent” comes from the Latin per centum, meaning “by the hundred.” Percentages make it easy to compare proportions across different sizes and are used everywhere in daily life — from shopping discounts and tip calculations to interest rates and statistics.
Common Percentage Calculations
1. Finding a Percentage of a Number
What is X% of Y? This is the most basic percentage calculation. Simply multiply the percentage (as a decimal) by the number:
Example: What is 15% of 80? Answer: 0.15 × 80 = 12
2. Finding What Percentage One Number Is of Another
X is what percent of Y? Divide the part by the whole and multiply by 100:
Example: 12 is what percent of 80? Answer: (12 / 80) × 100 = 15%
3. Percentage Increase
By what percent did the value increase from X to Y?Calculate the difference, divide by the original value, and multiply by 100:
Example: A stock goes from $50 to $65. Percentage increase = ((65 - 50) / 50) × 100 = 30%
4. Percentage Decrease
By what percent did the value decrease from X to Y?
Example: A product drops from $80 to $60. Percentage decrease = ((80 - 60) / 80) × 100 = 25%
Practical Uses for Percentage Math
- Shopping discounts: Calculate the sale price after a percentage off and compare deals.
- Tipping: Quickly figure 15%, 18%, or 20% tips at restaurants.
- Tax rates: Determine how much sales tax, income tax, or property tax you pay.
- Investments: Calculate returns, fees, and growth rates on savings or stocks.
- Recipes: Scale ingredients up or down by a percentage.
- Grades: Convert test scores to percentages.
- Budgeting: Allocate income by percentages (the popular 50/30/20 budget rule is 50% needs, 30% wants, 20% savings).
Mental Math Shortcuts
You do not always need a calculator. Here are quick tricks:
- 10%: Move the decimal point one place left. 10% of 250 = 25.
- 5%: Take 10% and divide by 2. 5% of 250 = 12.5.
- 15%: Add 10% + 5%. 15% of 250 = 25 + 12.5 = 37.5.
- 20%: Double 10%. 20% of 250 = 50.
- 25%: Divide by 4. 25% of 250 = 62.5.
- 50%: Divide by 2. 50% of 250 = 125.
- Reverse trick: X% of Y = Y% of X. 8% of 50 = 50% of 8 = 4. Handy when the reverse is easier to compute.
Frequently Asked Questions
Why is a percentage change different from the reverse?
This is a common source of confusion. A 25% increase from 100 to 125, followed by a 25% decrease from 125, lands at 93.75 — not back at 100. That is because the base value changed: 25% of 125 is larger than 25% of 100. Always calculate percentage change relative to the starting value.
What is the difference between percentage and percentile?
A percentage is a fraction out of 100 (like scoring 90% on a test). A percentile tells you what percentage of values fall below a given point (scoring in the 90th percentile means you scored better than 90% of people). They sound similar but measure different things.
How do I calculate percentage of a percentage?
Convert both percentages to decimals and multiply, then convert back to a percentage. For example, 20% of 30% = 0.2 × 0.3 = 0.06 = 6%. This is useful for understanding things like fees on top of interest rates.