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1. The Three Fundamental Percentage Formulas
The word percent originates from the Latin per centum, meaning “by the hundred.” Every practical percentage query comes down to one of three formulas:
Formula A: Finding P% of Number X
Result = (P / 100) × XExample: What is 18% of a $75 restaurant bill?
Calculation: (18 / 100) × 75 = 0.18 × 75 = $13.50 tip.
Formula B: What Percentage is Number X of Number Y?
Result % = (X / Y) × 100Example: You scored 42 points out of 50 on an examination. What is your grade?
Calculation: (42 / 50) × 100 = 0.84 × 100 = 84%.
Formula C: Percentage Increase or Decrease
Change % = [(New – Old) / Old] × 100Example: A company's stock price rises from $80 to $100. What is the percentage gain?
Calculation: [(100 – 80) / 80] × 100 = (20 / 80) × 100 = 0.25 × 100 = +25% increase.
2. Profit Margin vs. Markup: The Crucial Business Distinction
Entrepreneurs and retail managers frequently confuse profit margin and markup. While both express profit as a percentage, they use different denominators:
Profit Margin (% of Selling Price)
If an item costs $60 to manufacture and sells for $100, the profit is $40. The profit margin is ($40 / $100) × 100 = 40%. Profit margin can never exceed 100%.
Markup (% of Cost Price)
For the same product ($60 cost, $100 sale, $40 profit), the markup is ($40 / $60) × 100 = 66.67%. Markup indicates how much price is added on top of cost, and can easily exceed 100%.
3. Reverse Percentage: Finding the Original Price Before Discount
A jacket is on sale for $120 after a 20% discount. What was the jacket's original price before the sale?
A very common math trap is simply taking 20% of $120 ($24) and adding it back ($144). That is mathematically incorrect! The 20% discount was taken off the larger original price, not the sale price.
Original Price = $120 / (1 – 0.20) = $120 / 0.80 = $150.00.