Percentage change — quick, practical guide
Core idea
Percent change scales the difference between two values by the starting value to show growth or decline in context.
How it works
Formula: (New − Old) ÷ Old × 100%
- Positive → increase; negative → decrease; 0 → no change
- Multiplier = New ÷ Old; Percent = (Multiplier − 1) × 100%
Sanity checks
- Old must be ≠ 0
- Old → 2×Old → +100%
- Old → 0 → −100%
Shortcuts
- Relative change (decimal) = (New − Old) ÷ Old
- Chain changes multiply: ×1.10 then ×0.90 → overall ×0.99 (−1%)
Pitfalls
- Not symmetric: +25% then −25% ≠ 0%
- Small Old exaggerates percentages
Micro‑examples
- 50 → 75: (25/50)×100 = +50%
- 75 → 50: (−25/75)×100 = −33.33%
Mini‑FAQ
Over 100%? Yes—Old 10 → New 50 is +400%.
Action tip
Report both absolute change and percent change for clarity, e.g., “+25 (from 50 to 75), +50%.”