How to Calculate Percentages: Formulas and Examples
Easy formulas for percentage of a number, percentage change, increases, decreases and reverse percentages — with worked examples and common pitfalls.
“Per cent” means “per hundred”. Once you see a percentage as a fraction out of 100, every percentage problem becomes simple multiplication or division. Here are the formulas you need, with examples.
1. Find X% of a number
Formula: X% of Y = Y × X ÷ 100
Example: 20% of 1,500 = 1,500 × 20 ÷ 100 = 300.
Mental shortcut: 10% is the number divided by 10 (150), so 20% is double that (300), and 5% is half (75).
2. What percentage is X of Y?
Formula: (X ÷ Y) × 100
Example: You scored 72 out of 90. 72 ÷ 90 × 100 = 80%.
3. Percentage change
Formula: (New − Old) ÷ Old × 100
Example: Rent rose from 40,000 to 46,000. (46,000 − 40,000) ÷ 40,000 × 100 = +15%.
A negative result means a decrease: a price falling from 2,500 to 2,000 is −20%.
4. Increase or decrease by a percentage
Increase: Y × (1 + X ÷ 100). A salary of 80,000 with a 12% raise = 80,000 × 1.12 = 89,600.
Decrease: Y × (1 − X ÷ 100). A 3,000 item at 25% off = 3,000 × 0.75 = 2,250. For shop discounts, the Discount Calculator also handles stacked “extra % off” deals.
5. Reverse percentage (find the original)
If you know a value after a percentage change, divide — don’t subtract.
Example: A price including 18% GST is 11,800. Original = 11,800 ÷ 1.18 = 10,000. Subtracting 18% of 11,800 (2,124) would give 9,676 — wrong. The GST Calculator does this correctly.
Example: 45 is 15% of what? 45 ÷ 0.15 = 300.
Common pitfalls
Percentages are not reversible
A 50% fall followed by a 50% rise does not return you to the start: 100 → 50 → 75. The rise applies to a smaller base.
Successive discounts don’t add
“30% off plus an extra 20%” is 1 − (0.7 × 0.8) = 44% off, not 50%.
Percent vs percentage points
If an interest rate goes from 10% to 12%, it rose by 2 percentage points but by 20 percent. News reports often mix these up.
Margin vs markup
Buying at 800 and selling at 1,000 is a 25% markup (on cost) but a 20% margin (on price). The Profit and Loss Calculator shows both.
Quick reference
| Question | Formula |
|---|---|
| X% of Y | Y × X ÷ 100 |
| X is what % of Y | X ÷ Y × 100 |
| % change | (New − Old) ÷ Old × 100 |
| Increase Y by X% | Y × (1 + X/100) |
| Decrease Y by X% | Y × (1 − X/100) |
| Original before X% added | Total ÷ (1 + X/100) |
For instant answers with the working shown, use the Percentage Calculator.
Try the tools from this guide
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