Percentage Increase and Decrease Formula: How to Calculate Relative Change

Understanding relative change is critical in business analytics, personal investing, and data science. While absolute change tells you how much a number moved, percentage change explains the magnitude of that movement relative to where it started.

For example, a $10 price hike on a $20 item is a massive 50% increase, whereas a $10 hike on a $1,000 computer is a negligible 1% change.

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The Percentage Increase Formula

To calculate the percentage increase from an original value to a new value:

Percentage Increase = ((New Value - Original Value) ÷ Original Value) × 100

Step-by-Step Example

Scenario: A stock's share price rises from $80 to $100. What is the percentage increase?

1. Find the absolute difference:
   Difference = 100 - 80 = 20
2. Divide by the original value:
   20 ÷ 80 = 0.25
3. Multiply by 100:
   0.25 × 100 = 25%

Result: The stock increased by 25%.

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The Percentage Decrease Formula

When a quantity declines over time, the calculation follows the exact same logic:

Percentage Decrease = ((Original Value - New Value) ÷ Original Value) × 100

Step-by-Step Example

Scenario: A jacket originally priced at $120 is marked down to $90. What is the discount percentage?

1. Find the discount amount:
   Decrease = 120 - 90 = 30
2. Divide by the original price:
   30 ÷ 120 = 0.25
3. Multiply by 100:
   0.25 × 100 = 25%

Result: The jacket is discounted by 25%.

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The #1 Common Pitfall: The Asymmetry of Percentages

One of the most frequent mathematical mistakes people make is assuming percentage increases and decreases are symmetrical. They are not.

Consider this scenario:

1. You have $100.
2. It experiences a 50% loss: you now have $50.
3. It then gains 50%: $50 + 50% = $75$.

You do not break even! To return to your original $100 after a 50% drop, you need a 100% gain ($50 \times 2 = $100$). Always divide by the current baseline when calculating changes.

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Try It in the Browser

You can compute relative percentage growth and reductions instantly with our client-side Percentage Calculator.