Math

How to Calculate Percentage Increase, Decrease, and Relative Difference

Master the mathematical rules of percentage calculations with easy step-by-step formulas for discounts, sales tax, inflation rates, and business metrics.

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Prof. David ChenMathematics Educator & Author
Published 2026-02-18
4 min read

The Core Percentage Change Formula

Whenever you want to calculate how much a number has grown or declined relative to its original starting point, use the universal percentage change formula:

\text{Percentage Change (\%)} = \frac{\text{New Value} - \text{Old Value}}{|\text{Old Value}|} \times 100

* If the result is positive (+), you have a Percentage Increase. * If the result is negative (−), you have a Percentage Decrease.

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Step-by-Step Examples

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Example 1: Percentage Increase

Suppose your monthly SaaS software subscription increases from $40 to $50. 1. Difference: $50 - 40 = 10$. 2. Divide by original: $10 / 40 = 0.25$. 3. Multiply by 100: $0.25 \times 100 = \mathbf{25\%\text{ Increase}}$.

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Example 2: Percentage Decrease

A winter coat is marked down from $120 to $90. 1. Difference: $90 - 120 = -30$. 2. Divide by original: $-30 / 120 = -0.25$. 3. Multiply by 100: $-0.25 \times 100 = -25\% \rightarrow \mathbf{25\%\text{ Discount / Decrease}}$.

Frequently Asked Questions

Why does a 50% loss require a 100% gain to break even?

If you have $100 and lose 50%, you now have $50. To return to $100 from $50, you must gain $50 on your new $50 base, which is a 100% increase.