Percentages are everywhere — discounts, interest, exam marks, tips, tax, statistics — yet many people freeze the moment a calculation goes beyond "10% of something". The truth is that every percentage problem comes down to a handful of simple formulas, and once you can recognise which one a question is asking for, they all become easy. This guide walks through each type with a worked example, so you can handle any percentage that life throws at you.
The one idea behind all of it
"Per cent" literally means "per hundred". A percentage is just a fraction with 100 on the bottom: 25% means 25 out of 100, or 0.25 as a decimal. Every calculation below is really about converting between this fraction, its decimal, and a real quantity. If you remember only one thing, make it this: to turn a percentage into a decimal, divide by 100 (so 18% becomes 0.18), and to go back, multiply by 100. Nearly every formula flows from that.
Finding a percentage of a number
The most common task. To find X% of a number, multiply the number by X and divide by 100:
Result = Number × Percentage ÷ 100
For example, 15% of 800 = 800 × 15 ÷ 100 = 120. This is what you use for a tip, a commission, or "20% of the class". A handy trick: 15% of 800 is the same as 800% of 15 — percentages are reversible, so if one direction is easier to do in your head, flip it.
Working out what percentage one number is of another
Sometimes you have two numbers and want the percentage — for instance, you scored 42 out of 60 and want your percentage mark. Divide the part by the whole and multiply by 100:
Percentage = Part ÷ Whole × 100
So 42 ÷ 60 × 100 = 70%. The same formula tells you what proportion of a budget you have spent, or what share of a total a figure represents. The Percentage Calculator handles this and the previous case, so you can check any of them instantly.
Percentage increase and decrease
To increase a number by a percentage, find the percentage and add it on; to decrease, subtract it. A quicker method uses a multiplier: to add 20%, multiply by 1.20; to take off 20%, multiply by 0.80. So a ₹500 item after a 20% rise is 500 × 1.20 = ₹600, and after a 20% discount is 500 × 0.80 = ₹400. The multiplier method is faster and less error-prone, and it chains neatly: a 10% rise followed by a 10% fall is 1.10 × 0.90 = 0.99, so you end up 1% below where you started — which surprises people and explains why successive percentages don't simply cancel.
Percentage change between two values
To measure how much something has changed — a price, a salary, a population — use:
Percentage change = (New − Old) ÷ Old × 100
If a share rises from ₹250 to ₹300, the change is (300 − 250) ÷ 250 × 100 = +20%. A positive result is an increase, a negative one a decrease. The crucial detail is that you always divide by the old (original) value, not the new one — a mistake here is the most common percentage error of all. The Percentage Change Calculator does this for you and gets the direction right every time.
Reverse percentages: finding the original
This is the one that catches everyone out. Suppose a price is ₹590 after a 18% tax has been added, and you want the original pre-tax price. You cannot just subtract 18% of 590 — because the 18% was added to the smaller original, not to 590. Instead, recognise that ₹590 represents 118% of the original, and divide:
Original = Final ÷ (1 + percentage/100)
So original = 590 ÷ 1.18 = ₹500. The same logic works in reverse for discounts: if a sale price of ₹400 is after a 20% discount, the original was 400 ÷ 0.80 = ₹500. This reverse calculation is exactly what tax and discount tools automate — see the GST Calculator for extracting tax from an inclusive price and the Discount Calculator for working sale prices and savings both ways.
Percentage points vs percentages
One distinction causes endless confusion, especially in news and finance: the difference between a "percentage point" and a "percent". If an interest rate rises from 4% to 6%, that is an increase of two percentage points — but as a percentage change it is a 50% increase, because 2 is half of the original 4. Both statements are correct; they measure different things. A percentage point is the plain arithmetic gap between two percentages, while a percent change expresses that gap relative to the starting value. Whenever you read that something "rose 2 points" versus "rose 2 percent", check which is meant — the two can differ enormously, and the ambiguity is sometimes used to make a change sound bigger or smaller than it really is.
Mental-maths shortcuts
A few tricks make everyday percentages effortless. To find 10%, just move the decimal one place left (10% of 340 = 34). Then build from there: 5% is half of 10%, 20% is double it, 15% is 10% plus 5%. For 1%, move the decimal two places. So a 15% tip on a ₹340 bill is 34 + 17 = ₹51, done in your head. And remember the reversibility trick — 4% of 25 is fiddly, but 25% of 4 is obviously 1. With these, most real-world percentages need no calculator at all; keep the tools above for the trickier reverse and change calculations.
Key takeaways
- Percentage of a number = number × percent ÷ 100.
- Use multipliers for increase/decrease (×1.20 to add 20%, ×0.80 to subtract 20%).
- Percentage change always divides by the old value: (new − old) ÷ old × 100.
- For reverse percentages, divide by (1 + percent/100) — never just subtract the percent of the final amount.