The five formulas, in plain terms
Every percentage problem is the same fraction wearing different clothes. A percent is "per hundred", so 15% is 15/100 or 0.15.
- X% of Y:
X / 100 × Y. Fifteen percent of ₹2,400 is 0.15 × 2,400 = ₹360. - X as a percent of Y:
X / Y × 100. A score of 42 out of 60 is 0.7 × 100 = 70%. - Percentage change:
(new − old) / old × 100. The base is always the old value. - Reverse percentage: after a discount,
original = now / (1 − d/100). After an increase,original = now / (1 + d/100). - Successive discounts: multiply the remaining fractions,
final = price × (1 − d1/100) × (1 − d2/100) × ….
A worked example: the same ₹6,000 gives two different percentages
Say Riya's monthly salary goes from ₹40,000 to ₹46,000. The change is ₹6,000, and the base is the old salary: 6,000 / 40,000 = 0.15, a 15% increase.
Now suppose a pay cut takes her from ₹46,000 back to ₹40,000. The same ₹6,000 is now measured against ₹46,000: 6,000 / 46,000 = 0.1304, a 13.04% decrease. A rise of 15% is not undone by a fall of 15%. Put the two inputs in box 3 in either order and you will see it.
The same trap works with equal percentages. Start at ₹100, add 20% to get ₹120, then take off 20% and you land on ₹96, not ₹100. The second 20% is taken from a bigger number.
Mistakes that cost real money
Reversing a discount by adding it back. A shirt now costs ₹1,700 after a 15% discount. Many people compute 1,700 × 1.15 = ₹1,955 and call that the old price. The correct answer is 1,700 / 0.85 = ₹2,000, because the 15% was taken off the original, not off ₹1,700. Box 4 does this properly.
Adding successive discounts. A "20% + 10%" offer on a ₹2,000 item is not 30% off. Twenty percent takes ₹400 off, leaving ₹1,600. Ten percent of ₹1,600 is ₹160, leaving ₹1,440. That is 28% off in total. Add a third 5% and the effective discount becomes 31.6%, not 35%. The order does not change the result, but the gap between the simple sum and the true figure grows as the discounts get bigger.
Backing GST out the wrong way. If a ₹1,180 bill includes 18% GST, the pre-tax price is 1,180 / 1.18 = ₹1,000 and the GST is ₹180. Taking 18% of ₹1,180 gives ₹212.40 and a base of ₹967.60, which is wrong by about ₹32. The inclusive-price case is just box 4 with "Increase" selected. The GST calculator does the same thing with the CGST and SGST split.
Mixing up percent and percentage points. If a savings rate moves from 8% to 9%, that is 1 percentage point, but a 12.5% relative increase (1/8). News about interest rates, inflation and GST rates uses both loosely, so check which one is meant.
Using the wrong base in percentage change. "A is 25% more than B" and "B is 20% less than A" describe the same gap. Always say which number is the starting point.
Where the calculator stops
Everything here is simple arithmetic, so the limits are about interpretation, not accuracy. Percentage change from zero is undefined, so box 3 refuses it. If the old value is negative, such as a loss turning into a profit, the result is measured against the absolute size of the old number, which is a convention rather than a law, and different spreadsheets handle it differently. Results are rounded to two decimals for display. Do not use the percentage figure alone for loans or investments, where the percentage applies repeatedly over time; the compound interest and SIP calculator handles that. For a longer look at the habits behind these mistakes, read the percentage guide.
Questions people ask
How do I find the percentage increase between two numbers?
Subtract the old from the new, divide by the old, and multiply by 100. For ₹40,000 to ₹46,000 that is 6,000 / 40,000 × 100 = 15%.
Why is a 50% discount followed by 50% not free?
The second 50% applies to the already halved price. ₹1,000 becomes ₹500, then ₹250. The effective discount is 75%.
What is the difference between 10% off and ₹10 off?
A percentage scales with the price, a flat amount does not. On a ₹5,000 item, 10% off saves ₹500. On a ₹50 item, 10% saves only ₹5.
Can a percentage be more than 100?
Yes, for growth. A price that doubles has risen 100%, and one that triples has risen 200%. A discount, though, cannot exceed 100% because the price would go below zero.