Guides/Compound percentage increase (two steps)

Compound percentage increase over two steps

Two raises of 10% are not a 20% raise. Each step multiplies the current value, so the second percent applies to a new base. Same idea as stacking discounts in reverse.

The factor method

A change of p% means multiply by (1 + p/100). For a decrease, p is negative (or use 1 − p/100).

After two steps: final = start × (1 + p₁/100) × (1 + p₂/100). Overall percent change = (final ÷ start − 1) × 100.

Single-step increase formula:percentage increase. For discounts and “percent off,” seepercent off vs percent of.

Worked examples

1. +10% then +10%: Start $100 → ×1.10 = $110 → ×1.10 = $121. Overall +21%, not +20%.
2. +20% then −20%: $100 → $120 → ×0.80 = $96. Overall −4%, not back to $100.
3. Price then tax-like add: Item $80, +25% markup → $100; then +8% fee → $100 × 1.08 = $108. Combined factor 1.25 × 1.08 = 1.35 → +35% from $80.
4. Two decreases: $200, −10% then −10% → 200 × 0.9 × 0.9 = $162(−19% overall), not −20%.

Common mistakes

• Adding the percents (10+10=20) instead of multiplying factors.
• Applying the second percent to the original start, not the intermediate value.
• Confusing percentage points with compounded percent change.

Check each step

Use thePercentage Calculatorfor each step or to verify overall old → new percent change. Related:decrease & discount math. Pricing language:markup vs margin.