Percentage Formulas Explained: 5 Calculations You Use Every Week

The short answer

Almost every everyday percentage question is one of five calculations:

Question	Formula	Example
What is X% of Y?	Y × X ÷ 100	15% of 200 = 30
X is what % of Y?	X ÷ Y × 100	30 is 15% of 200
% change from X to Y	(Y − X) ÷ X × 100	80 → 100 is +25%
Add X% to Y	Y × (1 + X ÷ 100)	1,000 + 18% = 1,180
Subtract X% from Y	Y × (1 − X ÷ 100)	500 − 10% = 450

The free Percentage Calculator has a mode for each one, so you pick the question and type two numbers.

1. What is X% of Y?

"Percent" means "per hundred", so 15% is 15/100 = 0.15. To find 15% of 200, multiply: 200 × 0.15 = 30.

Quick mental trick: 10% of any number is that number with the decimal moved one place left. 10% of 4,350 is 435. From there, 5% is half of that (217.50) and 20% is double (870).

Everyday uses: tips, commissions, the interest component of a payment, how much of a ₹5,00,000 budget is 12%.

2. X is what percent of Y?

Divide the part by the whole and multiply by 100. If you scored 68 out of 80: 68 ÷ 80 × 100 = 85%.

The most common mistake is dividing the wrong way round. The "whole" goes on the bottom: the total marks, the total budget, last year's revenue.

Everyday uses: exam scores, what share of your salary goes to rent, what share of ad spend one campaign takes.

3. Percentage change

Percentage change compares a new value with an old one: (new − old) ÷ old × 100.

• A salary going from ₹50,000 to ₹56,000: (56,000 − 50,000) ÷ 50,000 × 100 = +12%.
• A price falling from ₹1,200 to ₹900: (900 − 1,200) ÷ 1,200 × 100 = −25%.

The asymmetry trap. A 25% fall followed by a 25% rise doesn't get you back to where you started. ₹1,200 down 25% is ₹900; ₹900 up 25% is ₹1,125. To recover a 25% fall you need a 33.3% rise, because the rise is calculated on the smaller number. This is why investment losses are harder to recover than they look.

Percent vs percentage points. If a loan rate moves from 8% to 9%, that's a rise of 1 percentage point, but a 12.5% increase in the rate itself (1 ÷ 8 × 100). News reports often mix the two.

4. Adding a percentage

To add 18% to ₹1,000, multiply by 1.18: ₹1,180. This is how GST, service charges and price hikes are applied.

Successive increases multiply, they don't add. Two 10% price rises are not a 20% rise: 100 × 1.10 × 1.10 = 121, a 21% increase overall.

5. Subtracting a percentage

To take 10% off ₹500, multiply by 0.90: ₹450. Discounts work this way.

Stacked discounts. "40% off plus an extra 10% off" is not 50% off. ₹1,000 × 0.60 × 0.90 = ₹540, which is 46% off. The Discount Calculator handles stacked discounts directly.

The reverse percentage: removing tax from a price

A very common question in India: "This costs ₹1,180 including 18% GST. What's the price before tax?"

The wrong answer is ₹1,180 − 18% = ₹967.60, because 18% was added to the original price, not to ₹1,180. The right answer divides by 1.18:

₹1,180 ÷ 1.18 = ₹1,000, so the GST is ₹180.

The same logic works for any "including X%" price: divide by (1 + X ÷ 100). The GST Calculator does inclusive and exclusive GST with the CGST/SGST split.

Worked examples

Exam marks: you need 40% to pass a 150-mark paper. 150 × 0.40 = 60 marks.

Salary hike: your CTC moves from ₹9,60,000 to ₹10,56,000. (10,56,000 − 9,60,000) ÷ 9,60,000 × 100 = 10% hike.

Ad budget share: one campaign spent ₹3,24,000 of a ₹12,46,000 monthly budget. 3,24,000 ÷ 12,46,000 × 100 = 26% of spend.

Restaurant bill with service charge and GST: ₹2,000 food, 5% GST. 2,000 × 1.05 = ₹2,100.

Weight change: 82 kg to 78 kg. (78 − 82) ÷ 82 × 100 = −4.9%.

Rounding

The calculator shows percentages to two decimal places. For money, round only the final answer, not intermediate steps; rounding each step of a multi-step calculation can drift by a rupee or two.

Percentage vs percentile

They sound alike but measure different things:

• Percentage is your score out of 100: 72 out of 90 is 80%.
• Percentile is your rank: the 90th percentile means you scored higher than 90% of test takers.

Competitive exams in India often report percentiles, which depend on how everyone else did. A 95 percentile could correspond to quite different raw percentages in two different years.

Growth over several years: why averages mislead

If an investment grows 50% one year and falls 20% the next, the "average return" of 15% a year is misleading. ₹1,00,000 × 1.5 × 0.8 = ₹1,20,000, which is 20% total over two years, or about 9.5% a year compounded.

The compounded yearly rate is called CAGR (compound annual growth rate):

CAGR = (end value ÷ start value)^(1 ÷ years) − 1

For ₹1,00,000 growing to ₹1,20,000 over 2 years: (1.2)^(0.5) − 1 = 0.0954, or 9.54% a year. The Compound Interest Calculator works this out for savings and investments.

Five mistakes to avoid

Dividing by the wrong base. Percentage change always divides by the original value.

Adding percentages that apply in sequence. Two 10% rises make 21%, not 20%.

Removing tax by subtracting the rate. Divide by (1 + rate) instead.

Comparing percentages of different totals. 50% of a small campaign's spend can be less money than 10% of a large one's. Look at the amounts too.

Confusing percent with percentage points. An interest rate moving from 7% to 9% rose by 2 percentage points, which is a 28.6% increase in the rate.

Related calculators

• Discount Calculator for sale prices and stacked offers
• GST Calculator for inclusive and exclusive GST
• EMI Calculator for loan payments, where interest is a percentage per month