How to Calculate Percentages (with Examples)
Master percentage calculations for tips, discounts, grade changes, and tax. Includes the three core formulas with worked examples.
Percentages are everywhere — tips at restaurants, sale discounts, tax rates, test scores, salary changes. Yet most people still reach for a calculator even for simple percentage math. Once you understand the three core formulas, you can do these calculations quickly in your head or on paper.
What is a percentage?
A percentage is a way of expressing a number as a fraction of 100. The word itself comes from the Latin *per centum*, meaning "by the hundred." When you say 25%, you mean 25 out of every 100, or 0.25 as a decimal.
The most important thing to understand is that percentages are always relative to something — a whole, a base, or a reference value. That context is what makes percentages meaningful.
The three core formulas
Formula 1: What is X% of Y?
This is the most common calculation — finding a percentage of a number. The formula is: Result = (X ÷ 100) × Y.
Example: What is 18% of $65 (a restaurant tip)?
- 18 ÷ 100 = 0.18
- 0.18 × 65 = $11.70
Example: What is 8.25% sales tax on a $120 item?
- 8.25 ÷ 100 = 0.0825
- 0.0825 × 120 = $9.90
Formula 2: X is what percentage of Y?
You use this when you know both numbers and want to find the ratio. Formula: Percentage = (X ÷ Y) × 100.
Example: You scored 43 out of 50 on a quiz. What percentage is that?
- 43 ÷ 50 = 0.86
- 0.86 × 100 = 86%
Example: A shirt is discounted from $80 to $60. What percentage did you save?
- You saved $20. That is the X value.
- 20 ÷ 80 = 0.25
- 0.25 × 100 = 25% off
Formula 3: X is Y% of what number?
The reverse calculation — finding the original whole. Formula: Original = X ÷ (Y ÷ 100).
Example: After a 15% discount, a jacket costs $68. What was the original price?
- $68 is 85% of the original (100% − 15% = 85%)
- Original = 68 ÷ 0.85 = $80
Example: You received a 20% raise and now earn $60,000. What was your salary before?
- $60,000 is 120% of the original salary
- Original = 60,000 ÷ 1.20 = $50,000
Percentage change formula
When you want to know how much something changed relative to where it started, use the percentage change formula:
Percentage Change = ((New Value − Old Value) ÷ Old Value) × 100
A positive result is a percentage increase. A negative result is a percentage decrease.
Example: A stock was $45 and is now $54. What is the percentage change?
- (54 − 45) ÷ 45 = 9 ÷ 45 = 0.20
- 0.20 × 100 = 20% increase
Example: A city's population fell from 250,000 to 235,000. What is the percentage change?
- (235,000 − 250,000) ÷ 250,000 = −15,000 ÷ 250,000 = −0.06
- −0.06 × 100 = −6% (a 6% decrease)
Worked examples for everyday situations
Restaurant tip: Your bill is $47.50 and you want to leave a 20% tip.
- 20% of $47.50 = 0.20 × 47.50 = $9.50 tip
- Total with tip: $47.50 + $9.50 = $57.00
Sale discount: A $120 coat is 30% off.
- Discount amount: 0.30 × 120 = $36
- Sale price: $120 − $36 = $84
Grade change: Your midterm score was 72% and your final was 88%. How much did you improve?
- Percentage change: (88 − 72) ÷ 72 × 100 = 16 ÷ 72 × 100 ≈ 22.2% improvement
Tax on a purchase: You are buying a $350 laptop with 7.5% sales tax.
- Tax: 0.075 × 350 = $26.25
- Total: $350 + $26.25 = $376.25
Common mistakes to avoid
Mistake 1: Confusing percentage points with percent change. If interest rates rise from 3% to 4%, that is a 1 percentage point increase — but a 33% increase in rate. These are very different things.
Mistake 2: Adding percentage discounts directly. A 20% discount followed by another 10% discount is NOT a 30% total discount. After 20% off: 80% remains. Then 10% off that: 80% × 0.90 = 72%. The total discount is 28%, not 30%.
Mistake 3: Using the wrong base. Percentage change always uses the starting value as the base, not the ending value. A price going from $100 to $50 is a 50% decrease — but going from $50 back to $100 is a 100% increase, not 50%.
Quick mental math tricks
For 10%: simply move the decimal point one place to the left. 10% of $85 = $8.50.
For 5%: find 10% then halve it. 5% of $85 = $4.25.
For 15% (tip): find 10% and add half again. 15% of $60 = $6 + $3 = $9.
For 20%: find 10% and double it. 20% of $75 = $7.50 × 2 = $15.
For 25%: divide by 4. 25% of $80 = $20.
For 50%: divide by 2. Simple.
For 1%: move the decimal two places left. 1% of $347 = $3.47.
These building blocks let you estimate most real-world percentages in a few seconds without needing paper or a calculator. If you want to run exact numbers quickly, try our percentage calculator — it handles all three formulas and percentage change in one place.
Try it yourself
Run the numbers with our interactive calculator — change any value and get instant results.
Open calculatorThis article is for informational and educational purposes only. Always verify calculations that matter with a qualified professional.