A percentage is just a fraction out of 100, which makes the maths far easier than it looks. Whether you are splitting a discount, checking an exam aggregate or comparing rent increases, the same three formulas cover almost every case.
The one formula that covers half of all percentage questions
Percent of a number. Multiply the number by the percentage divided by 100. Example: 12% of 45,000 = 45,000 × 12 / 100 = 5,400. A shop discount of 25% on a Rs 4,000 item means you save 4,000 × 0.25 = Rs 1,000.
Percentage change: increase and decrease
Change % = (new - old) / old × 100. A salary that rises from Rs 40,000 to Rs 46,000 increased by (6,000 / 40,000) × 100 = 15%. If the number drops, the same formula gives a negative result, which is usually read as a percentage decrease.
Reverse percentage (finding the original before a change)
If a price already includes a 16% increase and now stands at Rs 58,000, divide by 1.16 to get the original: 58,000 / 1.16 = Rs 50,000. Reverse percentages appear in GST-inclusive bills, salary hike letters and rent arrears - anywhere the change has already been applied.
Quick checks so the answer feels right
- 50% is half, 25% is a quarter, 10% is moving the decimal point once.
- Doubling an amount moves any percentage up by the same factor - 12% of 10 is 1.2, so 12% of 20 is 2.4.
- Percentages above 100% just mean the part is bigger than the whole: 150% of 20 is 30.
Example walk-through: an exam aggregate
Out of 500 marks you scored 423. Your percentage is 423 / 500 × 100 = 84.6%. Now suppose you want the score needed for 90%: 500 × 90 / 100 = 450 marks, so you need 27 more. For the increase and reverse cases, the free Percentage Calculator has dedicated modes so you never rearrange the formula by hand. The Discount Calculator handles sale-price maths including tax on top.