Percentage Increase vs Decrease

Both formulas compare a change to the original value. The difference is whether the value went up or down.

Percentage Increase

Use when the new value is greater than the old value (e.g. price went up, marks improved).

Formula: ((New − Old) ÷ Old) × 100

Example: Old price 50, new price 65. Increase = ((65 − 50) ÷ 50) × 100 = 30%.

Percentage Decrease

Use when the new value is less than the old value (e.g. discount, drop in score).

Formula: ((Old − New) ÷ Old) × 100

Example: Old price 80, new price 60. Decrease = ((80 − 60) ÷ 80) × 100 = 25%.

Summary

  • Increase: new > old → use (new − old) / old × 100
  • Decrease: new < old → use (old − new) / old × 100
  • In both cases the denominator is the original (old) value.

Use our Percentage Calculator →

Why a price hike followed by an equal discount does not cancel out

Increase and decrease look symmetric on paper but behave very differently because they use different bases. A 20% increase is computed on the old value; a 20% decrease on the same value would give back exactly the original amount. But a 20% increase followed by a 20% decrease on the new (larger) value lands you 4% below where you started: 1 × 1.20 × 0.80 = 0.96.

This is why "dearness allowance restored" news in Indian government circulars is sometimes misleading. A salary cut of 10% followed by a 10% restoration brings back only 99% of the original number. To get back to 100% after a 10% cut, you need a 11.11% raise.

Indian salary, sale and stock examples

₹50,000 cut by 10%, then raised 10%
50,000 × 0.90 × 1.10 = ₹49,500 (1% lower)
₹2,000 marked up 50%, then 50% off (Diwali sale)
2,000 × 1.50 × 0.50 = ₹1,500 (25% lower)
Stock falls 30%, then rises 30%
Net = down 9%; need a 42.86% rise to fully recover
Onion: ₹40 → ₹60 (50% rise) → back to ₹40
Decrease needed = 33.3%, not 50%

General rule: to recover an X% loss, you need a (X / (1 − X/100))% gain. A 50% crash needs a 100% rise to break even — which is why bear markets hurt long-term portfolios more than the headline percentage suggests.