Percentages are everywhere. From shopping discounts and exam scores to tax calculations and salary hikes — you encounter percentage calculations every single day. Yet many people find them confusing or reach for a calculator even for simple problems.
This guide breaks down everything you need to know about percentages — the formulas, step-by-step examples, common real-life applications, and mental math tricks that make calculations faster.
What is a Percentage?
A percentage is a way of expressing a number as a fraction of 100. The word “percent” comes from the Latin per centum, meaning “by the hundred.”
So when we say 45%, we mean 45 out of every 100 — or 45/100 = 0.45.
Percentages are used to compare values, express proportions, calculate changes, and describe ratios in a way that is easy to understand.
The Basic Percentage Formula
Percentage = (Part ÷ Whole) × 100
This one formula is the foundation of almost every percentage calculation you will ever need.
Example
You scored 72 marks out of 90 in an exam. What is your percentage?
Percentage = (72 ÷ 90) × 100 = 80%
5 Types of Percentage Calculations You Need to Know
Type 1 — What is X% of a Number?
Formula: Result = (X ÷ 100) × Number
Example: What is 15% of ₹8,000? Result = (15 ÷ 100) × 8,000 = 0.15 × 8,000 = ₹1,200
Real-life use: Calculating GST, tips, discounts, commission.
Type 2 — What Percentage is X of Y?
Formula: Percentage = (X ÷ Y) × 100
Example: 45 students passed out of 60. What percentage passed? Percentage = (45 ÷ 60) × 100 = 75%
Real-life use: Exam results, survey responses, conversion rates.
Type 3 — Percentage Increase
Formula: % Increase = [(New Value − Old Value) ÷ Old Value] × 100
Example: Your salary was ₹40,000 last year. This year it is ₹46,000. What is the percentage increase? % Increase = [(46,000 − 40,000) ÷ 40,000] × 100 = [6,000 ÷ 40,000] × 100 = 15%
Real-life use: Salary hikes, price increases, revenue growth.
Type 4 — Percentage Decrease
Formula: % Decrease = [(Old Value − New Value) ÷ Old Value] × 100
Example: A product was priced at ₹2,500. It is now selling for ₹2,000. What is the percentage decrease? % Decrease = [(2,500 − 2,000) ÷ 2,500] × 100 = [500 ÷ 2,500] × 100 = 20%
Real-life use: Discounts, price drops, expense reductions.
Type 5 — Finding the Original Value Before a Percentage Change
Formula: Original Value = Final Value ÷ (1 ± Percentage/100)
Use + for increase, − for decrease.
Example: After a 20% discount, a shirt costs ₹800. What was the original price? Original = 800 ÷ (1 − 20/100) = 800 ÷ 0.80 = ₹1,000
Real-life use: Finding the pre-discount price, pre-tax amount, original salary before deduction.
Percentage in Everyday Life — Real Examples
Shopping Discounts
A jacket is priced at ₹3,500 with a 30% discount. How much do you pay?
Discount amount = 30% of ₹3,500 = (30/100) × 3,500 = ₹1,050 Final price = ₹3,500 − ₹1,050 = ₹2,450
Quick method: Multiply the price by (1 − discount%). So ₹3,500 × 0.70 = ₹2,450.
GST Calculation
A product costs ₹5,000 before GST. GST rate is 18%. What is the final price?
GST amount = 18% of ₹5,000 = (18/100) × 5,000 = ₹900 Final price = ₹5,000 + ₹900 = ₹5,900
Quick method: Multiply the price by (1 + GST%). So ₹5,000 × 1.18 = ₹5,900.
Salary Hike
Your current salary is ₹55,000 per month. You receive a 12% hike. What is your new salary?
Hike amount = 12% of ₹55,000 = (12/100) × 55,000 = ₹6,600 New salary = ₹55,000 + ₹6,600 = ₹61,600
Exam Marks
You need 40% to pass an exam that is out of 150 marks. What is the minimum passing mark?
Passing marks = 40% of 150 = (40/100) × 150 = 60 marks
Bank Interest
You deposit ₹1,00,000 in a savings account at 4% annual interest. How much interest do you earn in one year?
Interest = 4% of ₹1,00,000 = (4/100) × 1,00,000 = ₹4,000
Percentage Comparison — Which is Bigger?
Sometimes you need to compare two percentages from different totals. The trick is to convert both to actual percentage values.
Example:
- Class A: 36 out of 45 students passed
- Class B: 52 out of 65 students passed
Class A pass %: (36/45) × 100 = 80% Class B pass %: (52/65) × 100 = 80%
Both classes have the same pass percentage — even though Class B had more students pass in absolute numbers.
Percentage Points vs Percentage Change
This is one of the most common sources of confusion when reading news or financial reports.
Percentage point = absolute difference between two percentages Percentage change = relative change expressed as a percentage
Example: Interest rates increased from 6% to 8%.
- The increase in percentage points = 8 − 6 = 2 percentage points
- The percentage change = [(8 − 6) ÷ 6] × 100 = 33.3%
Both statements are technically correct — but they mean very different things. Always check which one is being used when reading financial news.
Mental Math Tricks for Percentages
These shortcuts help you calculate percentages quickly in your head — no calculator needed.
10% Trick
To find 10% of any number, simply move the decimal point one place to the left.
- 10% of 850 = 85
- 10% of 3,200 = 320
5% Trick
5% = half of 10%. So find 10% first, then halve it.
- 5% of 850 = 85 ÷ 2 = 42.5
- 5% of 3,200 = 320 ÷ 2 = 160
1% Trick
To find 1%, move the decimal point two places to the left.
- 1% of 6,500 = 65
- 1% of 24,000 = 240
Building Any Percentage
Use combinations of 10%, 5%, and 1% to build any percentage quickly.
Example: Find 23% of ₹4,000
- 20% = 2 × 10% = 2 × 400 = 800
- 3% = 3 × 1% = 3 × 40 = 120
- 23% = 800 + 120 = ₹920
Reverse Percentage Trick
X% of Y = Y% of X
This is surprisingly useful:
- 8% of 50 = 50% of 8 = 4
- 16% of 25 = 25% of 16 = 4
- 75% of 48 = 48% of 75 = 36
Common Percentage Mistakes to Avoid
Mistake 1 — Confusing Percentage Increase and Decrease
If a price increases by 20% and then decreases by 20%, it does NOT return to the original value.
- Original: ₹1,000
- After 20% increase: ₹1,200
- After 20% decrease: ₹1,200 × 0.80 = ₹960 — not ₹1,000
Mistake 2 — Adding Percentages Directly
If you get a 10% discount and then an additional 10% discount, the total discount is NOT 20%.
- Original price: ₹1,000
- After first 10% discount: ₹900
- After second 10% discount: ₹900 × 0.90 = ₹810
- Actual total discount = (1,000 − 810) ÷ 1,000 × 100 = 19%, not 20%
Mistake 3 — Percentage vs Percentage Points
As explained earlier — a change from 5% to 7% is a 2 percentage point increase, but a 40% relative increase. These are not the same thing.
Use a Free Percentage Calculator
While mental math tricks are useful, a free online Percentage Calculator handles complex calculations instantly and eliminates errors. You can calculate:
- Percentage of a number
- Percentage increase or decrease
- What percentage one number is of another
- Original value before a percentage change
You can use the free Percentage Calculator on CalcBuddy Online to get instant, accurate results for any percentage problem — no sign-up required.
Frequently Asked Questions
Q: How do I calculate percentage without a calculator?
Use the 10%, 5%, and 1% tricks to build any percentage mentally. For example, 15% = 10% + 5%. Find each part separately and add them.
Q: How do I calculate a percentage increase in salary?
Use the formula: % Increase = [(New Salary − Old Salary) ÷ Old Salary] × 100.
Q: What is the difference between percentage and percentile?
Percentage is a score out of 100. Percentile tells you what percentage of people scored below you. A 90 percentile means you scored better than 90% of test takers — not that you got 90% marks.
Q: How do I find the original price before a discount?
Divide the discounted price by (1 − discount rate). For example, if a product costs ₹680 after a 15% discount: Original = 680 ÷ 0.85 = ₹800.
Q: How is GST calculated on a price?
Multiply the base price by the GST rate and add it to the base price. Or simply multiply by (1 + GST rate). For 18% GST on ₹1,000: ₹1,000 × 1.18 = ₹1,180.
Summary
Percentages are a fundamental part of everyday mathematics and financial literacy. Here is what to remember:
- Basic formula: Percentage = (Part ÷ Whole) × 100
- Finding X% of a number: (X ÷ 100) × Number
- Percentage increase: [(New − Old) ÷ Old] × 100
- Percentage decrease: [(Old − New) ÷ Old] × 100
- Finding original value: Final Value ÷ (1 ± rate/100)
- Use the 10%, 5%, and 1% tricks for fast mental calculations
- Do not confuse percentage points with percentage change
Once you are comfortable with these formulas and shortcuts, percentage calculations become fast, intuitive, and second nature.