How to Calculate Percentage: Every Type, Every Formula
Percentages appear everywhere — discounts, taxes, exam scores, interest rates, statistics. This guide covers every type of percentage calculation with clear formulas and worked examples.
What Is a Percentage?
A percentage is a number expressed as a fraction of 100. The word comes from the Latin per centum — "by the hundred." When we say 45%, we mean 45 out of every 100.
45% = (45) / (100) = 0.45
Type 1: Finding a Percentage of a Number
Question: What is X% of Y?
Formula:
Result = (X) / (100) × Y
Example: What is 15% of 80?
(15) / (100) × 80 = 0.15 × 80 = 12
Shortcut: Move the decimal point two places left to convert the percentage to a decimal, then multiply. 15% → 0.15 × 80 = 12.
Type 2: What Percentage Is X of Y?
Question: X is what percentage of Y?
Formula:
Percentage = (X) / (Y) × 100
Example: 18 is what percentage of 72?
(18) / (72) × 100 = 0.25 × 100 = 25%
Type 3: Percentage Increase
Question: What is the percentage increase from A to B?
Formula:
Increase = (B - A) / (A) × 100
Example: A price rises from $40 to $52. What is the percentage increase?
(52 - 40) / (40) × 100 = (12) / (40) × 100 = 30%
Type 4: Percentage Decrease
Question: What is the percentage decrease from A to B?
Formula:
Decrease = (A - B) / (A) × 100
Example: A salary drops from $60,000 to $54,000. What is the percentage decrease?
(60000 - 54000) / (60000) × 100 = (6000) / (60000) × 100 = 10%
Type 5: Percentage Change
Combines increase and decrease into one formula. Positive result = increase, negative = decrease.
Change = (New - Old) / (Old) × 100
Type 6: Finding the Original Value (Reverse Percentage)
Question: After a 20% increase, the price is $120. What was the original price?
This is the most commonly misunderstood type. Adding 20% means multiplying by 1.20. To reverse it, divide by 1.20 — not subtract 20%.
Original = (120) / (1.20) = 100
Common mistake: Subtracting 20% from $120 gives $96, not $100. That would be a 20% decrease from $120.
Type 7: Percentage Difference
Used when comparing two values without a clear "original" and "new" — for example, comparing two prices or two measurements.
Difference = (|A − B|) / ((A + B)/2) × 100
Example: Compare scores of 80 and 95.
(|80 − 95|) / ((80 + 95)/2) × 100 = (15) / (87.5) × 100 = 17.1%
Quick Mental Math Tricks
Find 10%: Move the decimal one place left. 10% of 450 = 45.
Find 5%: Halve the 10% value. 5% of 450 = 22.5.
Find 1%: Move the decimal two places left. 1% of 450 = 4.5.
Build any percentage from these:
- 15% = 10% + 5%
- 25% = 10% + 10% + 5%
- 30% = 10% × 3
- 17.5% (UK VAT) = 10% + 5% + 2.5%
Real-World Applications
Sales and discounts: A $250 jacket is 30% off. Discount = 0.30 × 250 = $75. Sale price = $250 − $75 = $175.
Tax: A $85 item with 8.5% tax. Tax = 0.085 × 85 = $7.23. Total = $92.23.
Exam scores: 34 correct out of 40 questions. Score = (34/40) × 100 = 85%.
Tip calculation: 20% tip on a $67.50 bill. Tip = 0.20 × 67.50 = $13.50.
Investment return: Portfolio grows from $10,000 to $13,400. Return = (13400 − 10000)/10000 × 100 = 34%.
Calculate Any Percentage Now
Our percentage calculator handles all seven types above. Enter your values and get the answer instantly with step-by-step working shown.