Percentages turn up in exam results, salary hikes, sale prices, loan rates, tips and test scores — and almost all of it comes down to three formulas. Learn those and you can do most of it in your head; the rest is arithmetic a calculator should handle. Here are the formulas, worked examples of every common case, and the two mistakes that cause the most confusion.
Quick answer: to find what percentage one number is of another, divide the part by the whole and multiply by 100. Percentage = (Part ÷ Whole) × 100. So 45 out of 60 is (45 ÷ 60) × 100 = 75%. For every other variation, the free Percentage Calculator shows the working alongside the answer.
1The three formulas that cover almost everything
“Per cent” literally means “per hundred”, so a percentage is just a fraction with 100 on the bottom. Every question below is one of these three:
(X ÷ Y) × 100
(P ÷ 100) × Y
((New − Old) ÷ Old) × 100
The third one is where people slip: the divisor is always the original value, not the new one, and not the difference.
2Worked examples of every common case
| Question | Working | Answer |
|---|---|---|
| What % is 45 out of 60? | (45 ÷ 60) × 100 | 75% |
| What is 20% of 500? | (20 ÷ 100) × 500 | 100 |
| What is 15% of 1,200? | 0.15 × 1,200 | 180 |
| Increase 250 by 20% | 250 × 1.20 | 300 |
| Decrease 80 by 25% | 80 × 0.75 | 60 |
| Change from 250 to 300 | ((300 − 250) ÷ 250) × 100 | +20% |
| Change from 80 to 60 | ((60 − 80) ÷ 80) × 100 | −25% |
| 45 is 15% of what number? | 45 ÷ 0.15 | 300 |
| Marks: 456 out of 500 | (456 ÷ 500) × 100 | 91.2% |
| ₹2,499 with 30% off | 2,499 − (0.30 × 2,499) | ₹1,749.30 |
3Percentage of marks
Exam percentages are the most-searched version of this question, and they are the simple case — total marks scored divided by total marks possible, times 100:
A student scoring 456 out of 500 gets 91.2%. Across subjects, add up everything first: 78 + 85 + 91 + 67 + 88 = 409 out of 500 = 81.8%. Do not average the subject percentages unless every subject carries the same maximum marks — with unequal maximums that shortcut gives the wrong answer.
The Marks Percentage Calculator handles subject-wise entry and the division ladder, and if your result is a CGPA rather than a percentage, the CGPA to Percentage Converter applies the right conversion for your board or university — the CBSE ×9.5 rule and the common (CGPA − 0.75) × 10 formula are not interchangeable.
4The two mistakes everyone makes
Percentage increase and decrease do not cancel out
Take 100, add 20% → 120. Now take 20% off 120 → 96, not 100. The percentages are calculated on different bases, so they never undo each other. This is why a 50% sale followed by a 50% price rise leaves the shop ahead, and why a stock that falls 50% needs to gain 100% to recover.
Percent vs percentage points. If an interest rate moves from 5% to 7%, that is a rise of 2 percentage points — but a 40% increase in the rate itself. News reports mix these up constantly. When the thing being measured is already a percentage, say “percentage points”.
Markup is not the same as margin
An item costs ₹800 and you add a 25% markup: 800 × 1.25 = ₹1,000 selling price. The profit is ₹200 — but as a margin that is 200 ÷ 1,000 = 20%, not 25%. Markup is measured against cost; margin is measured against the selling price. Confusing the two quietly wrecks pricing. The Profit Margin Calculator keeps them apart.
5Doing it in your head
- 10% is a decimal shift. 10% of 640 = 64. From there, 5% is half of that (32), 20% is double (128), and 30% is 64 × 3 = 192.
- Percentages are reversible. x% of y equals y% of x. 8% of 50 is awkward; 50% of 8 is obviously 4. Same answer, no effort.
- 1% is two decimal shifts. 1% of 2,450 = 24.5, so 3% = 73.5.
- Tips the easy way. 10% then half again gives 15%; on a ₹840 bill that is 84 + 42 = ₹126.
- Discounts: think of what’s left. 30% off means paying 70%, so multiply by 0.7 in one step instead of subtracting.
Fractions worth memorising
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 2/3 | 0.666… | 66.67% |
| 3/4 | 0.75 | 75% |
| 1/8 | 0.125 | 12.5% |
6Where percentages show up next
The Percentage Calculator covers seven modes — percentage of a number, what percent one value is of another, increase, decrease, percentage change, markup and discount — and shows the formula and steps for each, so it works as a check on your own arithmetic rather than a black box. For the specific jobs, use the Discount Calculator for sale prices, the GST Calculator when tax is added or removed from a total, and the EMI Calculator when the percentage is an interest rate — our guide to how EMI is calculated shows why the same rate produces very different totals over different tenures.
7Frequently Asked Questions
How do I calculate the percentage of a number?
Divide the percentage by 100 and multiply by the number. For 20% of 500: (20 ÷ 100) × 500 = 100. The shortcut is to multiply by the decimal — 0.20 × 500.
How do I calculate the percentage of marks?
Divide marks obtained by total marks and multiply by 100. Scoring 456 out of 500 gives (456 ÷ 500) × 100 = 91.2%. For several subjects, total everything first rather than averaging the individual percentages.
What is the formula for percentage increase?
((New value − Old value) ÷ Old value) × 100. Going from 250 to 300 is ((300 − 250) ÷ 250) × 100 = 20%. Always divide by the original value.
What is 20 percent of 500?
100. Multiply 500 by 0.20, or find 10% (50) and double it.
How do I find the original number before a percentage was added?
Divide by 1 plus the percentage as a decimal. If a price is ₹1,180 including 18% tax, the base is 1,180 ÷ 1.18 = ₹1,000. This is called a reverse percentage.
What is the difference between percentage and percentage points?
A move from 5% to 7% is 2 percentage points, but a 40% increase in the rate itself. Use “percentage points” whenever the quantity being compared is already a percentage.
Three formulas, and the rest is practice.
