What the formula calculates
A percentage expresses a fraction as a proportion of 100. The formula is Percentage = (Part / Whole) × 100. To find what percentage 45 is of 180: (45 / 180) × 100 = 25%. Percentages appear in discounts, tax rates, exam scores, financial margins, and statistical reporting.
Percentage change
Percentage change measures how much a value has increased or decreased relative to its original value: % Change = ((New Value - Old Value) / Old Value) × 100. A stock that rises from $80 to $96: % Change = (96 - 80) / 80 × 100 = 20% increase. A salary cut from $50,000 to $45,000: % Change = (45000 - 50000) / 50000 × 100 = -10%.
Reverse percentage (finding the original)
When a final value after a percentage increase or decrease is known, the original can be recovered: Original = Final / (1 + percentage/100) for an increase. A price of $85 after a 25% markup: Original = 85 / 1.25 = $68. A sale item at $63 after a 30% discount: Original = 63 / 0.70 = $90.
Common percentage traps
A 50% increase followed by a 50% decrease does not return to the original value. Starting at 100, +50% gives 150, then -50% of 150 gives 75. Percentage changes are not symmetric. Also, a change from 5% to 6% is a 1 percentage point increase but a 20% relative increase. These distinctions matter in financial and statistical analysis.