Percentage Increase — how much bigger is the new value?
Core idea
Percentage increase measures growth relative to the original value. It’s directional: order matters because the original is the baseline.
How it works
Formula: (New − Original) ÷ Original × 100.
- Compute the absolute increase Δ = New − Original
- Divide by the original value
- Multiply by 100 to get %
Sanity checks
- Original = 0 → undefined for finite New (division by 0)
- New = Original → 0%
- New = 2×Original → 100% increase
Shortcuts
- New = Original × (1 + r), where r is the rate as a decimal
- Original = New ÷ (1 + r)
- Growth factor = New ÷ Original = 1 + r
Pitfalls
- Mixing up percent increase with percentage points
- Applying r to the wrong base (use the original)
- Confusing a decrease with a negative increase
Micro‑examples
- 100 → 150: (50 ÷ 100) × 100 = 50%
- 80 → 92: (12 ÷ 80) × 100 = 15%
- Original 200, r = 12% → New = 200 × 1.12 = 224
Mini‑FAQ
- Can % increase exceed 100%? Yes (e.g., 10 → 50 is 400%)
- Compound vs simple? Compound applies the rate repeatedly over periods
- What if Original is 0? The increase % isn’t defined
Action tip
For planning: multiply the original by 1 + rate. For back-solving: divide the final by 1 + rate.