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How to calculate percentage increase and decrease

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Percentage change measures how much a value grows or shrinks relative to where it started. It is one of the most widely used mathematical concepts in finance, retail, science, and everyday life — whether you are tracking sales growth, comparing discounts, or analyzing quarterly inflation.

The most common mistake people make is calculating the change relative to the final value instead of the original starting value. Because the reference base shifts, an increase of 25% followed by a decrease of 20% brings you back to the exact starting number, while an increase of 50% followed by a decrease of 50% leaves you with a 25% net loss.

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Step by step

  1. Identify the starting value and ending value

    Clearly label the initial figure (V₁) and the new figure (V₂). For example, if a product price rose from $80 to $100, your starting value is $80 and your final value is $100.

  2. Subtract the starting value from the final value

    Calculate the absolute difference: ΔV = V₂ - V₁. In our example, 100 - 80 = 20. If the difference is positive, it represents an increase; if negative, it represents a decrease.

  3. Divide the difference by the starting value

    Divide ΔV by the original value V₁: 20 / 80 = 0.25. Always divide by where you started, never where you ended up.

  4. Multiply by 100 to convert to a percentage

    Multiply the decimal by 100: 0.25 × 100 = +25%. The price experienced a 25% increase.

Things worth knowing

  • The formula is: Percentage Change = ((New Value - Old Value) / Old Value) × 100.
  • A 100% increase means the value has doubled (2x original). A 200% increase means it has tripled (3x original).
  • Percentage decreases cannot exceed 100% unless dealing with negative values (e.g. debt or temperatures).
  • Percentage points are different from percentages: moving from 10% to 15% is a 5 percentage-point increase, but a 50% relative growth.

Frequently asked questions

Why does a 50% increase followed by a 50% decrease not equal 0% change?

Because the base changes. If you start with $100 and add 50%, you reach $150. If you then decrease $150 by 50%, you lose $75, leaving you with $75 — a 25% overall loss.

Can percentage change be negative?

Yes. A negative result simply indicates a percentage decrease. For instance, -15% indicates the quantity shrank by 15% from its original baseline.

How do I calculate what percentage one number is of another?

Divide the part by the whole and multiply by 100: (Part / Whole) × 100. For example, 25 out of 200 is (25 / 200) × 100 = 12.5%.

What is the difference between percentage and percentile?

A percentage is a proportion out of 100. A percentile is a statistical rank indicating the percentage of scores or observations that fall below a given value in a dataset.

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