Calculating a percentage is one of the most commonly used mathematical operations in daily life: commercial discounts, salary changes, statistics, school grades, interest rates... Mastering the different percentage formulas avoids common errors and confusion.
There are several types of percentage calculations depending on the need: calculating X% of a number, calculating what percentage A represents of B, calculating a percentage increase or decrease, calculating the percentage change between two values, or finding the original value before an increase/decrease.
📐 Formula
X% of N = N × X/100 | A is what % of B? = (A/B) × 100 | Value after +X% = N × (1 + X/100) | Change % = ((New - Old) / Old) × 100
📊 Reference table
| Calculation type | Formula | Example |
|---|---|---|
| X% of a number N | N × X / 100 | 15% of 80 = 12 |
| A is what % of B? | (A / B) × 100 | 30 is what % of 120 = 25% |
| Increase N by X% | N × (1 + X/100) | 200 + 15% = 230 |
| Decrease N by X% | N × (1 - X/100) | 200 - 20% = 160 |
| Change between A and B | ((B - A) / A) × 100 | (150-120)/120 = +25% |
| Price before X% discount | Sale price / (1 - X/100) | $80 after -20% → $100 |
💡 Practical examples
Example 1: 30% discount on an item priced at $79.99
Discount = 79.99 × 30% = $24.00. Final price = 79.99 × (1 - 0.30) = $55.99.
Example 2: salary increase from $2,500 to $2,750
Change = ((2,750 - 2,500) / 2,500) × 100 = (250/2,500) × 100 = 10% raise.
Example 3: find original price after 25% discount
Sale price = $45. Original price = 45 / (1 - 0.25) = 45 / 0.75 = $60.