SmartKitio

Mathematics & calculators · Updated 2026-10-04

Percentage Increase vs Percentage Decrease

Increase and decrease use the same change formula; only the direction of the result changes. The subtle part is what happens when you reverse a change: percentages are relative to the starting value of each step, so a rise and a fall of “the same percent” rarely cancel.

One formula, two directions

change % = ((new − old) ÷ old) × 100

If the result is positive, you have a percentage increase. If it is negative, you have a percentage decrease. In conversation people often report the absolute value and say “increased by” or “decreased by.”

Worked increase

Worked decrease

Percentage points vs percent

If a tax rate moves from 10% to 12%, the rate rose by 2 percentage points, which is a 20% relative increase of the old rate ((12 − 10) ÷ 10 × 100). Mixing these two languages is a common source of misleading headlines.

Same numbers, two readings

Old rateNew ratePercentage pointsRelative % change
10%12%+2 points+20%
5%4%−1 point−20%
50%60%+10 points+20%

Why reverses are not symmetric

Start with 100. Raise it by 50%: you get 150. Then lower 150 by 50%: you get 75, not 100. Each step uses a different base. To undo a +r% change you need a decrease of r / (1 + r/100) × 100 percent, not simply −r%.

  • Always write down the old value you are dividing by.
  • Say “percentage points” when you mean an absolute gap between two percents.
  • For discounts stacked in sequence, apply each factor to the current price, not to the original, unless the store states otherwise.

Try these SmartKitio tools

Use a tool when you want a result; keep this guide open when you want the method.

Browse family: Calculators

Related articles

Broader reading that connects to this guide—when the topic deserves more than a how-to.

  • Percentages in Everyday Life

    Tips, tax, discounts, interest, stats, and headlines—formulas, percentage points vs relative change, and worked examples you can verify.

Related guides