Percentage Calculator Guide: Every Formula You Need With Examples
From basic percentage to compound growth rates, this guide covers every percentage formula you need with worked examples and common real-world applications.
Basic Percentage — X% of a Number
The fundamental percentage calculation answers: what is X% of a given number? Convert the percentage to a decimal (divide by 100) and multiply. Examples: 15% of $240 = 0.15 × 240 = $36. 7.5% sales tax on a $120 item = 0.075 × 120 = $9 tax → $129 total. 22% of 85 test questions = 0.22 × 85 = 18.7 → 19 questions. Try our free percentage calculator to
Percentage Change (Increase & Decrease)
Percentage change measures how much a value has grown or shrunk relative to its starting point. A positive result is an increase; negative is a decrease. Examples: Stock price rises from $45 to $54 → change = ((54−45)/45) × 100 = +20%. Employee salary cut from $70,000 to $63,000 → change = ((63,000−70,000)/70,000) × 100 = −10%. Home value from $320
Percentage of a Total
This formula answers: what percentage does this part represent of the whole? Useful for grades, survey results, market share, budget allocation, and nutritional labels. Examples: A student scores 78 out of 95 points → (78/95) × 100 = 82.1%. A company spends $45,000 on marketing out of a $250,000 budget → (45,000/250,000) × 100 = 18%. A recipe calls
Reverse Percentage — Finding the Original Value
Reverse percentage answers: if a value after a percentage change is known, what was the original? This is essential for price-before-discount and pre-tax calculations. Examples: A shirt costs $68 after a 20% discount. Original price = $68 ÷ (1 − 0.20) = $68 ÷ 0.80 = $85. A price is $107.50 including 7.5% sales tax. Pre-tax price = $107.50 ÷ 1.075 =
Frequently Asked Questions
What is the formula for percentage increase?
Percentage increase = ((New Value − Original Value) ÷ Original Value) × 100. Always divide by the original (starting) value. For example, a price rising from $80 to $100 is a 25% increase: ((100−80)/80)×100 = 25%.
How do I calculate a percentage discount?
Discount amount = Original Price × (Discount% ÷ 100). Final price = Original Price × (1 − Discount%/100). Example: 30% off $150 → Discount = $150 × 0.30 = $45; Final price = $150 × 0.70 = $105. Or use our percentage calculator for instant results.
How do I add a percentage to a number?
To add X% to a number N, multiply N by (1 + X/100). Adding 8% to $200 = $200 × 1.08 = $216. Adding 7.5% sales tax to $89.99 = $89.99 × 1.075 = $96.74. This is faster than calculating the percentage first and then adding it.
What is the difference between percentage points and percent change?
Percentage points are absolute differences between percentages. Percent change is relative. If an interest rate rises from 4% to 6%, it increased by 2 percentage points — but that's a 50% relative increase ((6−4)/4 × 100). In financial and political reporting, confusing the two i
How do I calculate what percentage one number is of another?
Divide the part by the whole and multiply by 100. Example: 45 is what % of 180? Answer: (45/180) × 100 = 25%. Or: 73 correct answers out of 95 questions → (73/95) × 100 = 76.8%. This is the percentage of total formula.