Percentage Change Calculator

Understanding Percentage Change

Percentage change is a fundamental mathematical concept that describes the degree of change over time. It is used extensively in finance (stock returns, GDP growth), science (population change, chemical concentration), business (revenue growth, cost reduction), and everyday life (price changes, weight loss).

The Formula

Percentage Change = ((New Value - Old Value) / |Old Value|) × 100

The absolute value in the denominator ensures correct results even when working with negative starting values.

Example Calculations

• From 200 to 250: ((250-200)/200) × 100 = 25% increase
• From 500 to 400: ((400-500)/500) × 100 = -20% (20% decrease)
• From 75 to 90: ((90-75)/75) × 100 = 20% increase
• From 1000 to 1000: ((1000-1000)/1000) × 100 = 0% (no change)

Percentage Change vs. Percentage Difference

Percentage change is directional -- it matters which value is "old" and which is "new." Percentage difference is symmetric and uses the average of both values as the base. Use percentage change when you have a clear before-and-after relationship. Use percentage difference when comparing two independent values (like the height of two buildings).

Compounding Percentage Changes

Percentage changes do not simply add up. A 50% increase followed by a 50% decrease does not return you to the starting value. If you start with 100, a 50% increase gives 150, then a 50% decrease gives 75 -- which is 25% below where you started. This asymmetry is important in investing and financial planning.