Quick Answer: The 3 Core Percentage Formulas
Percentage simply means "per hundred" (from the Latin per centum). There are three common percentage calculations: 1. Finding percentage of a number: Value = (Percentage × Number) / 100 Example: What is 15% of ₹2,400? → (15 × 2400) / 100 = ₹360. 2. Finding what percentage one number is of another: Percentage (%) = (Part / Total) × 100 Example: You scored 420 out of 500 on an exam. What is your score? → (420 / 500) × 100 = 84%. 3. Finding percentage increase or decrease: Percentage Change (%) = [(New Value - Old Value) / Old Value] × 100 Example: A stock rises from ₹80 to ₹100. Percentage gain = [(100 - 80) / 80] × 100 = 25% increase.
How to Calculate Percentage Increase and Decrease
When comparing how much a quantity has grown or shrunk over time: Formula: Percentage Change = [(Final Value - Initial Value) / Initial Value] × 100 • If positive (+): Percentage Increase. • If negative (-): Percentage Decrease. Worked Example 1: Salary Hike Your monthly salary increases from ₹50,000 to ₹62,000: 1. Difference = ₹62,000 - ₹50,000 = ₹12,000 2. Divide by starting salary = ₹12,000 / ₹50,000 = 0.24 3. Multiply by 100 = 24% salary increase. Worked Example 2: Weight Loss Your body weight drops from 85 kg to 76.5 kg: 1. Difference = 76.5 - 85 = -8.5 kg 2. Divide by starting weight = -8.5 / 85 = -0.10 3. Multiply by 100 = -10% (a 10% decrease).
The Reversibility Trick: Mental Math Secret
Here is a mental math shortcut: X% of Y is always equal to Y% of X! x% of y = y% of x Suppose you need to calculate 16% of 50 in your head: Doing 16% of 50 feels complicated. But reverse it: 50% of 16 is half of 16, which is 8! Therefore, 16% of 50 is exactly 8. Similarly: • What is 18% of 25? Reverse it: 25% (one quarter) of 18 = 4.5. • What is 72% of 50? Reverse it: 50% of 72 = 36.
Profit Margin vs Markup: The Critical Business Difference
One of the most widespread financial errors made by retail business owners is confusing Markup Percentage with Profit Margin: • Markup: Percentage added to the cost price to determine selling price. Markup (%) = [(Selling Price - Cost Price) / Cost Price] × 100 • Profit Margin: Percentage of the selling price that is retained as profit. Profit Margin (%) = [(Selling Price - Cost Price) / Selling Price] × 100 Worked Example: A store buys an item for ₹100 and sells it for ₹150: • The gross profit in rupees is ₹50. • Markup = (₹50 / ₹100) × 100 = 50% markup. • Profit Margin = (₹50 / ₹150) × 100 = 33.33% margin! If a retailer aims for a 50% margin but mistakenly applies a 50% markup, they will earn significantly less revenue than budgeted.
Successive Percentage Changes: Why +20% Followed by -20% Loses Money
Many investors assume that if a stock goes up 20% on Monday and falls 20% on Tuesday, they are back at their starting capital. This is mathematically false. Watch what happens to a ₹1,00,000 investment: • Day 1: Asset gains 20%: ₹1,00,000 × 1.20 = ₹1,20,000. • Day 2: Asset drops 20%: ₹1,20,000 × 0.80 = ₹96,000! You have lost ₹4,00,000 (a net decline of 4%). Because the percentage drop applies to a larger base number, percentage reductions always outweigh equal percentage gains. To recover from a 50% portfolio crash, you need a 100% gain just to break even.
Percentages in Banking: Nominal APR vs Effective APY
When comparing financial products like fixed deposits or credit cards, understanding the difference between APR and APY prevents costly errors: • Annual Percentage Rate (APR): The nominal annualized interest rate without taking intra-year compounding into account. • Annual Percentage Yield (APY): The actual effective percentage return earned in a year after compounding interest is factored in. The mathematical relation is: APY = (1 + r / n)^n - 1 If a bank advertises an 8.00% annual interest rate on fixed deposits compounded quarterly (n = 4): APY = (1 + 0.08 / 4)^4 - 1 = (1.02)^4 - 1 = 1.0824 - 1 = 8.24% Your true annualized percentage yield is 8.24%, giving you a higher effective return than the nominal 8.00% headline figure.
Common Mistakes to Avoid With Percentages
1. The Asymmetric Percent Trap: Always remember that recovering from losses requires larger percentage gains than the original decline. 2. Percentage Points vs Percent: If interest rates climb from 5% to 6%, they increased by 1 percentage point, but the relative percentage increase was 20% [(6 - 5) / 5 × 100]. Confusing these terms creates false reporting in financial news.
Calculate All 3 Modes Online
You can calculate percentages of numbers, percentage change, and percentage shares using our free QuickCalc Percentage Calculator.