How to Calculate Percentage — 3 Formulas with Examples
Updated October 2026 · 4 min read
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The word percentage comes from the Latin per centum — "per hundred." A percentage is simply a fraction with 100 as the denominator. Once you understand the three core formulas, every percentage problem becomes straightforward.
Formula 1: What is X% of Y?
This is the most common type. You have a percentage and a number, and you want to find the portion.
Result = (X / 100) x Y
Example: What is 20% of 350?
= (20 / 100) x 350 = 0.20 x 350 = 70
Real-world use: Calculating a 20% discount on a $350 item — you save $70, so you pay $280.
Formula 2: X is What Percentage of Y?
You have two numbers and want to express the relationship as a percentage.
Percentage = (X / Y) x 100
Example: 45 is what % of 180?
= (45 / 180) x 100 = 0.25 x 100 = 25%
Real-world use: You scored 45 out of 60 on a test — that is 75%. Or: 12 of your 80 employees work remotely — that is 15%.
Formula 3: Percentage Change
Used to measure how much something increased or decreased relative to its original value.
% Change = ((New - Old) / |Old|) x 100
Example: Price rose from $80 to $100
= ((100 - 80) / 80) x 100 = 20 / 80 x 100 = +25%
A positive result is an increase; negative is a decrease. Divide by the absolute value of the old number so that a drop from -5 to -3 shows as an increase (+40%), which is mathematically correct.
Quick Mental Maths Shortcuts
| To find | Shortcut | Example (of 240) |
|---|---|---|
| 10% | Shift decimal left once | 24 |
| 5% | Half of 10% | 12 |
| 1% | Shift decimal left twice | 2.4 |
| 25% | Divide by 4 | 60 |
| 50% | Divide by 2 | 120 |
| 75% | Divide by 4, multiply by 3 | 180 |
Common Mistakes to Avoid
- Reversing a percentage: A 50% increase followed by a 50% decrease does not return to the original. $100 +50% = $150, then -50% = $75.
- Percentage vs. percentage points: If a tax rate rises from 10% to 15%, it rose by 5 percentage points, but by 50% relative to the old rate.
- Dividing by the wrong base: For percentage change, always divide by the old value, not the new one.
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