How to Calculate Percentage Increase, Decrease & Percentage Points
Percentages are one of the most widely used mathematical concepts in finance, retail shopping, medicine, and business analytics. Yet, percentage calculations are also where people make the most frequent and costly mistakes.
Written by the Toolseza team · Updated 2026-10-06
The core formula for percentage change
Percentage change measures the relative difference between an original starting value and a new final value. The mathematical formula is: Percentage Change = ((New Value - Old Value) / Old Value) × 100.
A positive result indicates a percentage increase, whereas a negative result reflects a percentage decrease. The most common error is dividing by the new value instead of the original baseline. Always divide by the starting point.
Why increases and decreases are never symmetrical
A fundamental truth of mathematics is that percentage increases and decreases do not mirror each other. If an investment falls by 50% from £100 to £50, it does not require a 50% increase to recover; it requires a 100% gain (£50 to £100) just to break even.
Similarly, in retail, if an item is marked up by 25% and subsequently discounted by 25%, the final price is lower than the original cost: £100 + 25% = £125; £125 - 25% = £93.75. Understanding this asymmetry prevents costly misjudgments in trading and pricing.
Percentage versus percentage points
Confusing a percentage with a percentage point is a widespread error in financial journalism and political debate. A percentage point is the simple arithmetic difference between two percentage figures.
For example, if a central bank raises benchmark interest rates from 4% to 5%, the rate has increased by 1 percentage point. However, in relative terms, the interest rate itself rose by (5 - 4) / 4 × 100 = 25%. Stating that rates rose by "1%" when borrowing costs jumped 25% creates immense misunderstanding.
Working backwards: Reverse percentages
To find the original price of an item before a percentage was added (such as calculating the pre-tax price of a product including 20% VAT), never subtract 20% from the total. Instead, divide the total price by (1 + rate): £120 / 1.20 = £100.
For items after a discount, divide the sale price by (1 - discount rate). If a coat costs £75 after a 25% reduction, the original price was £75 / 0.75 = £100.