How Each Formula Works
X% of Y — multiply Y by X, then divide by 100. Useful for discounts, tips, and tax calculations.
X is what % of Y — divide X by Y, then multiply by 100. Useful for finding what share one number is of another, like marks scored out of total marks.
% Change from X to Y — subtract X from Y, divide by X, then multiply by 100. A positive result means an increase; a negative result means a decrease. Useful for tracking price changes, salary hikes, or growth rates.
A Practical Example for Each Mode
For example, imagine a restaurant bill of ₹1,500 and you want to leave a 10% tip. Using the first formula: 1,500 × 10 ÷ 100 = ₹150. Add that to your bill, and you're paying ₹1,650 in total.
Let's say you scored 78 marks out of 90 on an exam and want to know your percentage. Using the second formula: 78 ÷ 90 × 100 = 86.67%. This same formula works for anything expressed as "part of a whole" — a discount amount relative to original price, or a completed task count relative to a total.
Imagine your monthly rent went from ₹18,000 to ₹20,000. Using the third formula: (20,000 − 18,000) ÷ 18,000 × 100 = 11.11%. Your rent increased by roughly 11%.
A Common Mistake: Mixing Up Percentage Change and Percentage Points
A typical mistake we often see involves confusing a percentage change with a change measured in percentage points, especially when the original number is itself a percentage. Say an interest rate moves from 5% to 7%. That's a change of 2 percentage points, but expressed as a percentage change, it's actually a 40% increase (since 2 ÷ 5 × 100 = 40). Both statements are technically correct, but they mean very different things, and mixing them up in a financial or business context can lead to real misunderstandings about the size of a change.
Why the Order of X and Y Matters
One common scenario: someone accidentally swaps X and Y in the percentage-change formula and gets a confusing result. The formula specifically measures change relative to the starting value (X), not the ending value (Y) — this is why going from 100 to 150 is a 50% increase, but going back from 150 to 100 isn't a 50% decrease, it's a 33.3% decrease. The asymmetry surprises people the first time they encounter it, but it makes sense once you remember that percentage change is always measured against the original starting point, not the new one.
Everyday Situations Where These Formulas Come in Handy
A small business owner calculating a seasonal discount, a student checking their exam percentage, someone comparing this year's salary hike to last year's, or a shopper working out how much a "20% off" sale actually saves in rupees — all of these boil down to one of these three basic formulas. Many freelancers also use the percentage-change formula regularly, for example when comparing month-over-month income to see whether a particular client relationship or income stream is growing or shrinking over time.