Percentages are everywhere – exam marks, salary hikes, discounts, GST, loan rates and investment returns. Yet many people are unsure how to calculate percentage correctly, especially for increases, decreases and reverse percentages. This guide gives you every percentage formula you need, with clear worked examples, shortcuts for mental maths, and how to do the same calculations on a calculator or in Excel.
What Is a Percentage?
"Per cent" means "per hundred". A percentage is a way of writing a number as a fraction of 100. So 25% means 25 out of 100, which is the same as the fraction 1/4 or the decimal 0.25. Because everything is compared with 100, percentages make it easy to compare values of different sizes – for example, 45 marks out of 60 and 70 out of 100.
The Basic Percentage Formula
Percentage = (Part ÷ Whole) × 100
Almost every percentage problem is a rearrangement of this one formula. Once you know two of the three values – the part, the whole and the percentage – you can find the third.
How to Find a Percentage of a Number
Value = (Percentage ÷ 100) × Number
Example: what is 18% of ₹2,500? 18 ÷ 100 × 2,500 = ₹450. This is how you find the percentage of a number – useful for tax, tips and commissions.
Quick mental shortcuts
- 10 percent of any number: move the decimal point one place left. 10% of 850 = 85.
- 20 percent of a number: find 10% and double it. 20% of 850 = 170.
- 5%: half of 10%. 5% of 850 = 42.5.
- 25%: divide by 4. 50%: divide by 2. 1%: divide by 100.
- Percentages are reversible: 8% of 50 is the same as 50% of 8 = 4.
X Is What Percent of Y?
Percentage = (X ÷ Y) × 100
Example: 45 is what percent of 60? 45 ÷ 60 × 100 = 75%. This answers questions like "what share of my salary goes on rent?" or "x is what percent of y?"
How to Calculate Percentage of Marks
To work out the percentage of marks, divide the total marks you scored by the maximum marks and multiply by 100.
Marks % = (Marks obtained ÷ Total marks) × 100
Example: you scored 437 out of 500 in five subjects. 437 ÷ 500 × 100 = 87.4%. That is how to calculate marks percentage for board exams, college results and competitive exams. If subjects have different maximum marks, add up all marks obtained and all maximum marks first – do not average the individual percentages.
CGPA to percentage
CBSE suggests an indicative formula for CGPA to percentage conversion: multiply the CGPA by 9.5. A CGPA of 8.6 becomes 8.6 × 9.5 = 81.7%. Universities often use their own formulas, so always check the conversion rule printed on your grade card.
Percentage Increase and Decrease
Percentage change = (New value − Old value) ÷ Old value × 100
A positive answer is a percentage increase; a negative answer is a percentage decrease. This is the percentage change formula.
- Increase example: a price rises from ₹500 to ₹650. (650 − 500) ÷ 500 × 100 = 30% increase.
- Decrease example: a stock falls from ₹80 to ₹60. (60 − 80) ÷ 80 × 100 = −25%, a 25% decrease.
- Percentage of salary increase: salary goes from ₹6,00,000 to ₹6,60,000. The hike is ₹60,000 ÷ ₹6,00,000 × 100 = 10%.
Always divide by the old (starting) value. Dividing by the new value is the most common percentage mistake.
Adding or Subtracting a Percentage
To increase a number by a percentage, multiply by (1 + rate ÷ 100). To decrease it, multiply by (1 − rate ÷ 100).
- ₹2,000 + 15% = 2,000 × 1.15 = ₹2,300
- ₹2,000 − 15% = 2,000 × 0.85 = ₹1,700
Reverse Percentage: Finding the Original Value
A reverse percentage question asks for the value before a percentage was added or taken off.
Original = Final value ÷ (1 ± rate ÷ 100)
Example: a bill of ₹1,180 includes 18% GST. The price before GST is 1,180 ÷ 1.18 = ₹1,000 – not ₹1,180 minus 18%. The same idea finds the original price before a discount. For GST specifically, try our GST calculator.
Percentage Difference
Percentage difference compares two values when neither is the "starting" one, such as prices at two shops:
% difference = |A − B| ÷ ((A + B) ÷ 2) × 100
For ₹40 and ₹50: 10 ÷ 45 × 100 = 22.2%.
Discount, Profit and Loss Percentage
Discount percentage
Sale price = marked price × (1 − discount ÷ 100). A 30% discount on ₹2,499 gives 2,499 × 0.70 = ₹1,749.30. To find the discount percentage from two prices: (marked price − sale price) ÷ marked price × 100.
Profit and loss percentage
Profit percentage = (selling price − cost price) ÷ cost price × 100. If you buy for ₹800 and sell for ₹1,000, the profit is 200 ÷ 800 × 100 = 25%. Loss percentage uses the same formula with a negative result. Note that profit percentage is based on cost, while margin is based on the selling price – 25% profit on cost equals a 20% margin.
Percent vs Percentage Points
When a rate changes from 6% to 8%, it has risen by 2 percentage points but by 33.3% in relative terms. News reports and loan offers often mix the two. Use percentage points for the simple gap between two percentages.
Converting Fractions, Decimals and Percentages
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333 | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 3/4 | 0.75 | 75% |
Percent to decimal: divide by 100 (37.5% = 0.375). Fraction to percentage: divide the top by the bottom and multiply by 100 (3/8 = 37.5%). For exact fraction work, use our fraction calculator.
How to Calculate Percentage on a Calculator and in Excel
On a calculator
To find 18% of 2,500 on a calculator, type 2500 × 18 % – most calculators show 450. To add 18%, type 2500 + 18 % = 2,950. Our free online calculator has a percentage key that works this way.
Percentage in Excel
- Percentage of a number:
=A2*B2(with B2 formatted as a percentage, e.g. 18%). - What percent A is of B:
=A2/B2, then format the cell as a percentage. - Percentage change:
=(B2-A2)/A2, formatted as a percentage. - Add a percentage:
=A2*(1+B2); remove it:=A2/(1+B2).
Successive Percentage Changes
When one percentage change follows another, you cannot simply add them. Multiply the growth factors instead:
Final = Original × (1 ± r₁ ÷ 100) × (1 ± r₂ ÷ 100)
- A salary that rises 10% one year and 10% the next grows by 1.10 × 1.10 = 1.21, a total of 21%, not 20%.
- A shop that offers 20% off and then another 10% off at the till gives 0.80 × 0.90 = 0.72, a total discount of 28%, not 30%.
- A 20% rise followed by a 20% fall gives 1.20 × 0.80 = 0.96 – a 4% loss overall.
The same idea is behind compound interest, where each year's growth is applied to the new, larger balance. See it in action with our compound interest calculator.
Practice Questions with Answers
- What is 15% of 640? 640 × 0.15 = 96.
- A student scores 342 out of 400. What is the percentage? 342 ÷ 400 × 100 = 85.5%.
- Rent rises from ₹12,000 to ₹13,200. What is the percentage increase? 1,200 ÷ 12,000 × 100 = 10%.
- After a 25% discount a shirt costs ₹900. What was the original price? 900 ÷ 0.75 = ₹1,200.
- A shopkeeper buys at ₹1,250 and sells at ₹1,000. What is the loss percentage? 250 ÷ 1,250 × 100 = 20% loss.
- What percent of 80 is 12? 12 ÷ 80 × 100 = 15%.
Common Percentage Mistakes
- Dividing by the new value instead of the original when calculating change.
- Thinking a 20% rise followed by a 20% fall brings you back to the start – ₹100 → ₹120 → ₹96.
- Subtracting a percentage from a total to find the original (use division instead).
- Averaging percentages from groups of different sizes.
Frequently Asked Questions
How do I calculate percentage?
Divide the part by the whole and multiply by 100. For example, 45 out of 60 is 45 ÷ 60 × 100 = 75%.
How do I calculate the percentage of marks?
Add up the marks you scored, divide by the total maximum marks and multiply by 100. 437 out of 500 is 87.4%.
What is the formula for percentage increase?
Percentage increase = (new value − old value) ÷ old value × 100. A rise from 500 to 650 is a 30% increase.
How do I convert CGPA to percentage?
CBSE's indicative formula is CGPA × 9.5, so a CGPA of 8.6 is about 81.7%. Check your university's own formula if it provides one.
How do I find the original price before a percentage was added?
Divide the final price by (1 + rate ÷ 100). A price of ₹1,180 including 18% GST was ₹1,000 before GST.
What is 10 percent of 850?
85. To find 10% of any number, move the decimal point one place to the left.
What is the difference between percent and percentage points?
Percentage points are the simple difference between two percentages; percent is the relative change. A rise from 6% to 8% is 2 percentage points, or 33.3%.
Note: Examples are rounded to one or two decimal places. CGPA conversion rules vary by board and university – follow the rule stated by your institution.