“Per cent” means “out of 100”. The three core formulas: X% of Y = Y × X ÷ 100 (15% of 2,400 = 360); what percent X is of Y = X ÷ Y × 100 (45 of 60 = 75%); percentage change = (new − old) ÷ old × 100 (40 → 50 = +25%). For reverse percentages, divide: a price of 1,150 including 15% tax was 1,150 ÷ 1.15 = 1,000 before tax.
Percentages turn up everywhere: discounts, exam marks, pay rises, tax, interest, statistics in the news. You don’t need many formulas to handle them. Seven cover almost everything, and most are variations of the first two.
1. Find X% of a number
Result = number × percent ÷ 100
15% of 2,400 = 2,400 × 15 ÷ 100 = 360.
Mental shortcut: 10% is the number with the decimal point moved one place left. 10% of 2,400 is 240, 5% is half of that (120), so 15% = 360.
2. What percent is one number of another?
Percent = part ÷ whole × 100
You scored 45 out of 60: 45 ÷ 60 × 100 = 75%.
3. Percentage increase or decrease
Change = (new − old) ÷ old × 100
Rent goes from 40,000 to 46,000: (46,000 − 40,000) ÷ 40,000 × 100 = +15%.
A price falls from 2,500 to 2,000: (2,000 − 2,500) ÷ 2,500 × 100 = −20%.
Always divide by the old value. That’s the starting point the change is measured from.
4. Add a percentage
New = number × (1 + percent ÷ 100)
A 12% pay rise on 85,000: 85,000 × 1.12 = 95,200.
5. Take a percentage off
New = number × (1 − percent ÷ 100)
25% off 3,600: 3,600 × 0.75 = 2,700. The discount calculator handles “extra 10% off sale prices” too.
6. Reverse percentage: find the original
Original = final ÷ (1 ± percent ÷ 100)
A price of 1,150 includes 15% tax. The price before tax is 1,150 ÷ 1.15 = 1,000, not 1,150 − 15% (which would give 977.50).
A sale price of 2,700 is after 25% off. The original was 2,700 ÷ 0.75 = 3,600.
7. Percentage points vs percent
If an interest rate goes from 10% to 12%, it rose by 2 percentage points, which is a 20% increase in the rate (2 ÷ 10). News reports mix these up all the time. When comparing two percentages, say “points” for the simple difference.
The two classic traps
Up and down by the same percent doesn’t cancel
A share price rises 50% from 100 to 150, then falls 50%: 150 × 0.5 = 75. You’re down 25%, not back to 100. Percentages after the first one apply to a different base.
Percentages don’t add across different bases
A 20% discount followed by another 10% off is not 30% off. It’s 1 − (0.8 × 0.9) = 28% off. Similarly, two 10% pay rises in a row give 21%, not 20%.
Weighted percentages: marks with different weights
Many courses weight parts differently, for example assignments 20%, mid-term 30%, final exam 50%. Multiply each score by its weight and add them up:
Assignments 72%, mid-term 65%, final 80%: 0.2 × 72 + 0.3 × 65 + 0.5 × 80 = 14.4 + 19.5 + 40 = 73.9%.
A plain average of the three scores would give 72.3%, which is wrong here, because the final counts for half the grade. The average calculator page explains weighted averages in more detail, and the GPA calculator applies credit-hour weights for you.
Quick reference
| Question | Formula | Example |
|---|---|---|
| X% of Y | Y × X ÷ 100 | 15% of 2,400 = 360 |
| X is what % of Y | X ÷ Y × 100 | 45 of 60 = 75% |
| % change | (new − old) ÷ old × 100 | 40 → 46 = +15% |
| Add X% | Y × (1 + X/100) | 85,000 + 12% = 95,200 |
| Subtract X% | Y × (1 − X/100) | 3,600 − 25% = 2,700 |
| Remove tax of X% | Y ÷ (1 + X/100) | 1,150 ÷ 1.15 = 1,000 |
Where you’ll use these
- Exam marks and CGPA conversions
- Pricing and margin vs markup
- Loans and savings: compound interest
- Tax: adding or removing GST, VAT or sales tax
Frequently asked questions
How do I calculate a percentage of a number?
How do I calculate percentage increase?
How do I find the original price before a percentage was added?
Is 20% off and then 10% off the same as 30% off?
What is the difference between percent and percentage points?
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