Percentage Increase Classic

The percentage increase between two values is calculated as: ((New - Original) / |Original|) * 100. This tells you how large the increase is relative to the starting point. The absolute value in the denominator handles cases where the original is negative. This calculation is conceptually the inverse of the 'apply a percentage increase' operation. If you know the rate and want the result, you use New = Original * (1 + p/100). If you know both values and want the rate, you use p = ((New - Original) / Original) * 100. Together, these two operations form a complete toolkit for percentage increase problems. The percentage increase is always measured relative to the original value. This is important because the same absolute increase represents different percentage increases depending on the starting point. An increase of $100 is a 100% increase on a base of $100, but only a 10% increase on a base of $1,000. This relativity is why percentages are more informative than absolute changes for comparing across different scales. In finance, the percentage increase from a purchase price to a sale price is the return on investment (ROI). A stock bought at $50 and sold at $65 has a return of (65-50)/50 * 100 = 30%. This same logic applies to real estate appreciation, business revenue growth, and personal net worth tracking. Historically, percentage increases are used to track trends over time: year-over-year sales growth, quarterly earnings improvement, population growth rates, and inflation. These time-series percentages allow meaningful comparisons across different time periods and different scales of operation.