Percentage calculations are among the most common mathematical tasks in business, finance, and daily life. The fundamental formula for percentage change is: Percentage Change = ((New Value - Old Value) / |Old Value|) x 100.
If the result is positive, it represents a percentage increase; if negative, a percentage decrease. For example, if a price increases from $80 to $100: ((100 - 80) / 80) x 100 = (20 / 80) x 100 = 25% increase.
Markup vs Margin: a critical distinction
Markup and gross profit margin are frequently confused because both measure profit relative to cost and selling price, but they use different denominators. Cost = $60, Selling Price = $100, Profit = $40.
Markup is profit relative to cost: Markup = (Profit / Cost) x 100 = ($40 / $60) x 100 = 66.67%. Margin is profit relative to selling price: Margin = (Profit / Selling Price) x 100 = ($40 / $100) x 100 = 40.00%. A 50% markup yields a 33.3% margin; a 100% markup (keystone pricing) yields a 50% margin.
Calculating reverse percentages
A common mistake occurs when trying to find the original price before a discount or tax. If an item costs $85 after a 15% discount, the original price is NOT $85 x 1.15 = $97.75.
The correct formula for reverse percentage: Original Value = Final Value / (1 - Discount Rate). For $85 after a 15% discount: $85 / (1 - 0.15) = $85 / 0.85 = $100.00. Reversing a tax or price reduction requires dividing by the remaining percentage, not multiplying.