💡 Key Takeaways
- Percentage = (Part ÷ Whole) × 100 — that single formula covers almost every question.
- For marks: divide your score by the total marks, then multiply by 100.
- To find 15% of a number, find 10% and 5% separately and add them.
- Percentage increase compares the change to the original value, not the new one.
- Percentage points and percent are not the same thing — mixing them up is the most common mistake.
Percentage is one of those topics that shows up everywhere — school report cards, college admission forms, government job applications, bank interest, discounts, GST and even your phone's battery indicator. Yet most people still reach for a calculator app for something they could solve in five seconds.
This guide breaks percentage down into a handful of simple methods. Once you understand the core formula, the rest is just variations of the same idea.
What Is a Percentage?
The word "percent" literally means "per hundred" (from the Latin per centum). So when you say 45%, you mean 45 out of every 100.
A percentage is simply a fraction with a denominator of 100. That is why ½ = 50%, ¼ = 25%, and ¾ = 75% — because those fractions convert neatly into hundredths.
The Basic Percentage Formula
Everything in this article comes back to one formula:
Read it as: "divide what you have by the total, then shift the decimal two places to the right."
You scored 45 out of 60 in a test. What is your percentage?
(45 ÷ 60) × 100 = 0.75 × 100 = 75%
Method 1: Find the Percentage of a Number
This is the "what is 30% of 250?" type of question. Here you already know the percentage and need the actual value.
- Convert the percentage into a decimal by dividing it by 100. So 30% becomes 0.30.
- Multiply that decimal by the number. 0.30 × 250 = 75.
- Done — 30% of 250 is 75.
A shirt costs ₹1,800 and there is a 25% discount. How much do you save?
(25 ÷ 100) × 1800 = 0.25 × 1800 = ₹450 saved
Final price = 1800 − 450 = ₹1,350
Method 2: Convert Marks into Percentage
This is the most common use for students. The logic is identical to Method 1, just rearranged.
You got 78 out of 100 in Maths.
(78 ÷ 100) × 100 = 78%
Marks: English 82/100, Hindi 74/100, Science 88/100, Social Science 79/100, Maths 91/100.
Total obtained = 82 + 74 + 88 + 79 + 91 = 414
Total maximum = 5 × 100 = 500
(414 ÷ 500) × 100 = 82.8%
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Method 3: Percentage Increase and Decrease
Here you compare a new value against an old one. The key point: you always divide by the original value.
Your salary went from ₹25,000 to ₹30,000. What is the hike?
((30000 − 25000) ÷ 25000) × 100 = (5000 ÷ 25000) × 100 = 20% increase
A phone's price dropped from ₹18,000 to ₹15,300. What is the discount percentage?
((15300 − 18000) ÷ 18000) × 100 = (−2700 ÷ 18000) × 100 = 15% decrease
Method 4: Reverse Percentage — Find the Original Number
Sometimes you know the final value and the percentage applied, but not the starting number. This comes up in GST, discounts and exam cut-offs.
After a 25% increase, a price becomes ₹1,250. What was the original price?
1250 ÷ 1.25 = ₹1,000
Percentage vs Percentage Points
These two sound similar but mean very different things, and newspapers and reports mix them up constantly.
- Percentage point — the simple arithmetic difference between two percentages.
- Percent — the relative change between them.
A scheme's coverage rose from 40% to 45% of the population.
Rise in percentage points = 45 − 40 = 5 percentage points
Relative increase = (5 ÷ 40) × 100 = 12.5%
Both statements are correct — they just describe different things.
Quick Mental Math Tricks
You do not always need a calculator. These shortcuts handle most everyday situations.
1. The 10% anchor
To find 10% of any number, just move the decimal point one place to the left. 10% of 480 = 48.
2. Build from 10% and 1%
- 5% = half of 10%
- 1% = move the decimal two places left
- 15% = 10% + 5%
- 20% = double the 10% value
Find 15% of 240.
10% of 240 = 24 · 5% of 240 = 12
15% = 24 + 12 = 36
3. Flip the numbers
x% of y = y% of x. So 8% of 50 is the same as 50% of 8 — which is obviously 4. This trick turns awkward percentages into easy ones.
4. Use fraction equivalents
Common percentages are just friendly fractions. Recognising them saves a lot of time.
| Fraction | Percentage | Fraction | Percentage |
|---|---|---|---|
| 1/2 | 50% | 1/8 | 12.5% |
| 1/3 | 33.33% | 1/10 | 10% |
| 1/4 | 25% | 1/20 | 5% |
| 1/5 | 20% | 2/5 | 40% |
| 1/6 | 16.67% | 3/4 | 75% |
Common Mistakes to Avoid
- Dividing by the wrong number. The denominator is always the total, never the part.
- Averaging percentages of different totals. Weight them by the totals instead.
- Adding percentages of different bases. 10% of 100 plus 10% of 500 is not 20% of anything.
- Confusing percent with percentage points, as explained above.
- Rounding too early. Keep the full value until the final step, then round. Otherwise small errors snowball.
- Forgetting the ×100. Dividing alone gives you a decimal, not a percentage.
Frequently Asked Questions
What is the formula to calculate percentage?
How do I calculate the percentage of a number quickly?
What is the difference between percentage and percentage points?
How do I find the original number before a percentage increase?
Can I calculate percentage without a calculator?
Final Thoughts
Percentage is not a topic to memorise — it is a single formula applied in different directions. Get comfortable with (Part ÷ Whole) × 100, learn the 10% anchor trick, and be careful about what counts as the "original" value in increase/decrease questions. That covers almost everything you will ever need.
When the numbers get messy or you need an instant, error-free answer, use our free Percentage Calculator — no login, no signup, works on any device.