Percentage Change: Increase, Decrease, and Difference
Percentage calculations appear everywhere — price changes, salary negotiations, investment returns, and statistics. Three related but distinct concepts cause the most confusion: percentage increase, percentage decrease, and percentage difference.
Percentage Increase
% increase = [(New − Old) ÷ Old] × 100
Example: Price rises from £40 to £52
% increase = [(52 − 40) ÷ 40] × 100 = 30%Percentage Decrease
% decrease = [(Old − New) ÷ Old] × 100
Example: Price falls from £80 to £60
% decrease = [(80 − 60) ÷ 80] × 100 = 25%Percentage Difference (Between Two Values)
% difference = [|V1 − V2| ÷ ((V1 + V2) ÷ 2)] × 100
Use when neither value is the clear "reference" point
Example: 70 vs 90 → |70−90| ÷ 80 × 100 = 25%Common Mistakes
- Asymmetry: A 50% increase then a 50% decrease does not return to the original. £100 → £150 → £75.
- Reference point matters: A price rise from £80 to £100 is +25% from old to new, but −20% from new to old.
- Percentage points vs percent: A rate rising from 2% to 3% is an increase of 1 percentage point but 50% in relative terms.
Calculate percentage changes: Free Percentage Calculator