Percentage Change: How to Calculate Increases, Decreases, and Differences

Sales are up 23% year-over-year. Your investment lost 12% last quarter. The population grew by 8% over the decade. Percentage change is everywhere — and it's surprisingly easy to calculate incorrectly.

The Percentage Change Formula

Percentage change = ((New Value - Old Value) ÷ Old Value) × 100

Positive result = increase. Negative result = decrease.

Example 1: Your salary went from $55,000 to $62,000.

= ((62,000 - 55,000) ÷ 55,000) × 100 = (7,000 ÷ 55,000) × 100 = 12.7% increase

Example 2: Stock price fell from $140 to $112.

= ((112 - 140) ÷ 140) × 100 = (-28 ÷ 140) × 100 = -20% (20% decrease)

The Common Mistake: Which Number Is the Base?

The most frequent percentage change error: using the wrong number as the denominator.

Always divide by the original (starting) value — not the new value, not the average.

Wrong: Price changed from $80 to $100. Change = (100-80) ÷ 100 = 20%. Incorrect — used new value as base.

Right: (100-80) ÷ 80 = 25%. Correct — used original value as base.

Asymmetry of Percentage Changes

An important concept many people miss: a 50% decrease followed by a 50% increase does NOT bring you back to the original value.

Start: $100

After 50% decrease: $50

After 50% increase: $75

You're still down 25% from the original.

This is why investment losses require proportionally larger gains to recover:

Percentage Point vs. Percentage Change

These are not the same thing — and confusing them leads to significant errors.

Percentage points: Arithmetic difference between two percentages.

Percentage change: Relative change between two percentages.

Example: Interest rate rises from 4% to 6%.

• Percentage point change: 6% - 4% = 2 percentage points
• Percentage change: (6-4) ÷ 4 × 100 = 50% increase

Politicians and media often blur this distinction. When someone says "unemployment rose by 2%," they may mean 2 percentage points (e.g., 5% to 7%) — not that unemployment increased by 2% of itself (which would mean 5% to 5.1%).

Calculate any percentage change with our Percentage Calculator.