Your salary went from ₹6L to ₹7.2L. That's a 20% increase. But when you compare ₹6L and ₹7.2L as two independent values, the percentage difference is only 18.2%. Same numbers, different answer. Use the wrong one and you misrepresent everything.
The Three Formulas
| Name | Formula | When to Use | |------|---------|------------| | Percentage Increase | ((New − Old) ÷ Old) × 100 | Old → New change (direction matters) | | Percentage Decrease | ((Old − New) ÷ Old) × 100 | Old → New drop (direction matters) | | Percentage Difference | (|A − B| ÷ Average) × 100 | Comparing two values (no direction) |
The Trench Truth: Percentage increase and percentage difference are NOT interchangeable. Increase divides by the OLD value (the starting point). Difference divides by the AVERAGE of both values. When the two numbers are far apart, the results diverge wildly. A change from 10 to 50 is a 400% increase but only a 133% difference. The "400%" sounds dramatic because you're dividing by the small starting number. The "133%" is the neutral comparison. Neither is wrong — they answer different questions.
Percentage Increase: "How much did it go UP?"
Percentage Increase = ((New − Old) ÷ Old) × 100
📊 Salary Hike Examples
| Old Salary | New Salary | Increase | % Increase | |-----------|-----------|---------|-----------| | ₹4,00,000 | ₹4,80,000 | ₹80,000 | 20% | | ₹6,00,000 | ₹7,20,000 | ₹1,20,000 | 20% | | ₹8,00,000 | ₹10,00,000 | ₹2,00,000 | 25% | | ₹10,00,000 | ₹13,00,000 | ₹3,00,000 | 30% |
📊 Price Rise Examples
| Item | Old Price | New Price | % Increase | |------|----------|----------|-----------| | Petrol (₹/L) | ₹96 | ₹102 | 6.25% | | Milk (₹/L) | ₹54 | ₹60 | 11.1% | | Onion (₹/kg) | ₹30 | ₹80 | 166.7% | | House rent | ₹15,000 | ₹18,000 | 20% |
Calculate increases with our Percentage Increase Calculator.
Percentage Decrease: "How much did it go DOWN?"
Percentage Decrease = ((Old − New) ÷ Old) × 100
| Old | New | Decrease | % Decrease | |-----|-----|---------|-----------| | ₹1,000 | ₹800 | ₹200 | 20% | | ₹500 | ₹375 | ₹125 | 25% | | 100 marks | 65 marks | 35 marks | 35% | | 80% attendance | 60% | 20% | 25% |
📊 The Asymmetry Problem
A 20% increase does NOT undo a 20% decrease:
| Scenario | Calculation | Result | |---------|------------|--------| | Start: 100 → 20% increase | 100 × 1.20 | 120 | | Start: 100 → 20% decrease | 100 × 0.80 | 80 | | 80 → back to 100 | (100−80)÷80 × 100 | 25% increase needed | | 120 → back to 100 | (120−100)÷120 × 100 | 16.7% decrease needed |
The Trench Truth: If your portfolio drops 50%, you need a 100% gain to recover. If it drops 20%, you need a 25% gain. The math is brutal and asymmetric — losses require proportionally larger gains to recover. This is why investment advisors say "protect the downside" — a 10% loss needs only 11.1% to recover, but a 50% loss needs 100%. Calculate your investment returns with our Compound Interest Calculator.
Percentage Difference: "How different are these two things?"
Percentage Difference = (|A − B| ÷ ((A + B) ÷ 2)) × 100
This divides by the average of both values, making it symmetric — swapping A and B gives the same result.
📊 Comparing Two Offers
| Offer A | Offer B | |A−B| | Average | % Difference | |---------|---------|---------|---------|-------------| | ₹5,00,000 | ₹6,00,000 | ₹1,00,000 | ₹5,50,000 | 18.2% | | ₹8,00,000 | ₹10,00,000 | ₹2,00,000 | ₹9,00,000 | 22.2% | | ₹12,00,000 | ₹15,00,000 | ₹3,00,000 | ₹13,50,000 | 22.2% |
📊 Diagram: Which Formula Answers Which Question
┌──────────────────────────────────────────────────────────────┐
│ WHICH PERCENTAGE FORMULA TO USE? │
├──────────────────────────────────────────────────────────────┤
│ │
│ "How much did it INCREASE?" │
│ → % Increase = (New−Old)÷Old × 100 │
│ → Salary hikes, price rises, score improvements │
│ → Direction matters: Old is the baseline │
│ │
│ "How much did it DECREASE?" │
│ → % Decrease = (Old−New)÷Old × 100 │
│ → Price drops, score declines, budget cuts │
│ → Direction matters: Old is the baseline │
│ │
│ "How DIFFERENT are these two values?" │
│ → % Difference = |A−B|÷Average × 100 │
│ → Comparing two job offers, two cities, two products │
│ → No direction: A and B are equals, no baseline │
│ │
│ ⚠️ NEVER use % difference when there's a clear │
│ before/after relationship. Use % increase/decrease. │
│ │
└──────────────────────────────────────────────────────────────┘
Common Mistakes
📊 Mistake 1: Using Wrong Baseline
| Statement | Wrong | Right | Why | |-----------|-------|-------|-----| | "Rent went from ₹15K to ₹18K" | 18÷18×100 = 0% | (18−15)÷15×100 = 20% | Divide by OLD, not NEW | | "Price dropped from ₹100 to ₹80" | 80÷100×100 = 80% | (100−80)÷100×100 = 20% | That's the remaining %, not the decrease |
📊 Mistake 2: Adding Percentages
| Scenario | Wrong | Right | |---------|-------|-------| | 10% hike then 10% hike | 10+10 = 20% | 1.10 × 1.10 = 1.21 → 21% | | 20% discount then 15% discount | 20+15 = 35% | 0.80 × 0.85 = 0.68 → 32% | | 30% gain then 30% loss | 30−30 = 0% | 1.30 × 0.70 = 0.91 → 9% loss |
📊 Mistake 3: Confusing % Increase with % Difference
| Values | % Increase (A→B) | % Difference | Gap | |--------|-----------------|-------------|-----| | 100 → 200 | 100% | 66.7% | 33.3% | | 100 → 500 | 400% | 133.3% | 266.7% | | 100 → 1000 | 900% | 163.6% | 736.4% |
The further apart the values, the more these diverge.
Key Takeaways
- % Increase = (New−Old)÷Old × 100 — for before→after changes
- % Difference = |A−B|÷Average × 100 — for comparing two independent values
- A 20% drop needs a 25% gain to recover — percentage change is asymmetric
- Never add consecutive percentages — 10% + 10% ≠ 20% (it's 21%)
- Always divide by the OLD value for increase/decrease, not the new value
- Calculate any change: Percentage Increase Calculator | Percentage Change Calculator | Percentage Difference Calculator | Compound Interest Calculator
Related articles: Percentage Formula with 10 Examples | Attendance Percentage Guide | BMI Calculator
Sources: NIST Statistical Reference, CBSE Mathematics Curriculum, BLS Consumer Price Index Methodology, Khan Academy Percentage Change Lessons.
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