Percentage rules: every formula you actually need
Percentages are everywhere — sales, salary increases, VAT, marks, interest rates, tips. The maths is simple, but the four common variants trip people up. Here's each one with a worked South African example.
Updated By the ZACalc team
1. Finding X% of a number
The textbook formula: (percent ÷ 100) × value. Or shift the decimal two places: 15% becomes 0.15.
Example: A R1 200 jacket is on sale at 25% off. The discount is 0.25 × 1 200 = R300, so you pay R900.
2. X is what % of Y (the ratio)
Divide the part by the whole, then multiply by 100: (X ÷ Y) × 100.
Example: You scored 68 out of 80 in a test. (68 ÷ 80) × 100 = 85%.
3. Percentage change (increase or decrease)
((new − old) ÷ old) × 100. A negative answer means a decrease.
Example: Your salary moves from R28 000 to R31 000. ((31 000 − 28 000) ÷ 28 000) × 100 = +10.71%.
4. Reversing a percentage (the VAT trick)
The classic mistake: a price includes 15% VAT, you want the original. Don't subtract 15% — divide by 1.15. Original = total ÷ (1 + rate).
Example: A till slip shows R230 including VAT. Original = 230 ÷ 1.15 = R200. VAT portion = R30. Subtracting "15% of R230" gives R195.50, which is wrong.
Quick mental shortcuts
- 10% — move the decimal one place left.
- 5% — half of 10%.
- 20% — double 10%.
- 15% tip — 10% + half of 10%.
- VAT (15%) — multiply by 0.15 to add, divide by 1.15 to extract.
Compounding warning
A 10% rise followed by a 10% fall does not get you back to where you started. R1 000 → +10% = R1 100 → −10% = R990. Always re-base the percentage on the new value.