📈 What is X% of Y?
X is What % of Y?
Percentage Change
How to Calculate Percentages
Percentages are one of the most commonly used mathematical concepts in everyday life. From shop discounts to interest rates, tax calculations to exam grades, understanding percentages is a fundamental skill. The word "percent" simply means "per hundred" — so 15% means 15 out of every 100.
The Three Percentage Formulas
1. Finding X% of Y
This is the most common percentage calculation. Divide the percentage by 100, then multiply by the number.
Example: 20% of 350 = (20 / 100) × 350 = 70
2. Finding What Percentage X is of Y
Divide the part by the whole and multiply by 100.
Example: 45 is what % of 300? = (45 / 300) × 100 = 15%
3. Percentage Change (Increase or Decrease)
Subtract the old value from the new value, divide by the old value, and multiply by 100.
Example: From 80 to 100 = ((100 - 80) / 80) × 100 = +25% increase
Common Percentage Calculations
| Scenario | Formula | Example |
|---|---|---|
| Add a percentage | Number × (1 + %/100) | £100 + 20% = £100 × 1.20 = £120 |
| Subtract a percentage | Number × (1 - %/100) | £100 - 15% = £100 × 0.85 = £85 |
| Find original (before increase) | Number / (1 + %/100) | £120 before 20% markup = £120 / 1.20 = £100 |
| Find original (before discount) | Number / (1 - %/100) | £85 before 15% discount = £85 / 0.85 = £100 |
Percentage Tips and Shortcuts
- 10% shortcut: Move the decimal point one place left. 10% of 456 = 45.6
- 5% shortcut: Find 10% and halve it. 5% of 456 = 22.8
- 1% shortcut: Move the decimal two places left. 1% of 456 = 4.56
- Swap trick: X% of Y = Y% of X. So 8% of 50 = 50% of 8 = 4 (much easier!)
- Percentage points vs percentage: If a rate changes from 5% to 8%, that is a 3 percentage point increase but a 60% percentage increase. These are very different things and commonly confused in the media.
Real-World Uses of Percentages
- Shopping: Calculating discounts, VAT, and cashback offers
- Finance: Interest rates, investment returns, inflation
- Employment: Pay rises, bonus calculations, pension contributions
- Health: Body fat percentage, nutrient daily values, risk statistics
- Education: Exam scores, grade boundaries, attendance rates
- Business: Profit margins, growth rates, market share
Compound Percentages
A common mistake is assuming that percentages can be simply added or subtracted. If an investment grows by 10% in year one and 10% in year two, the total growth is NOT 20%. It is actually 21%, because the second 10% is applied to the larger amount:
- Start: £100
- After Year 1 (+10%): £110
- After Year 2 (+10%): £121 (10% of 110 = 11, not 10)
- Total growth: 21%, not 20%
This is the principle of compound interest, and it works in reverse too. If something drops by 50% and then rises by 50%, you do NOT get back to where you started — you are at 75% of the original value.
Frequently Asked Questions
Divide the percentage by 100, then multiply by the number. 15% of 200 = (15/100) × 200 = 30.
Divide the part by the whole and multiply by 100. 30 out of 200 = (30/200) × 100 = 15%.
((New - Old) / Old) × 100. From 50 to 75 = ((75-50)/50) × 100 = +50%.
Increase: multiply by (1 + X/100). Decrease: multiply by (1 - X/100). 200 + 15% = 200 × 1.15 = 230.