Triple Discount Calculator

Triple discounts are calculated by applying each discount sequentially to the price AFTER the previous discount. THE FORMULA: Final Price = Original × (1 - d₁) × (1 - d₂) × (1 - d₃). Where d₁, d₂, and d₃ are the discounts as decimals. STEP-BY-STEP EXAMPLE: Original price: $100. First discount: 20%. Second discount: 15%. Third discount: 10%. Step 1: $100 × 0.80 = $80 (after 20% off). Step 2: $80 × 0.85 = $68 (after additional 15% off). Step 3: $68 × 0.90 = $61.20 (after additional 10% off). Final price: $61.20. EQUIVALENT SINGLE DISCOUNT: Equivalent = 1 - (1 - d₁)(1 - d₂)(1 - d₃). = 1 - (0.80)(0.85)(0.90). = 1 - 0.612. = 0.388 or 38.8%. So 20% + 15% + 10% stacked = 38.8% total (NOT 45%). THE CUMULATIVE EFFECT: After 1st discount (20%): Cumulative 20% off. After 2nd discount (15%): Cumulative 32% off. After 3rd discount (10%): Cumulative 38.8% off. Each additional discount has diminishing absolute impact because it's applied to an already-reduced base.

The simple addition (45%) is wrong because each successive discount is applied to a smaller base, not the original price. THE MATHEMATICAL EXPLANATION: First discount (20%): Applied to $100 → Saves $20 (full 20% of original). Second discount (15%): Applied to $80 (not $100!) → Saves $12 (only 12% of original). Third discount (10%): Applied to $68 (not $100!) → Saves $6.80 (only 6.8% of original). Total savings: $20 + $12 + $6.80 = $38.80 (38.8%, not 45%). WHERE THE "MISSING" 6.2% WENT: You "lose" discount on the money you already saved. The 15% discount doesn't apply to the $20 you saved. The 10% discount doesn't apply to the $32 you already saved. The lost amount = 15% × $20 + 10% × $32 = $3 + $3.20 = $6.20. GENERAL FORMULA: For three discounts: Actual = d₁ + d₂ + d₃ - d₁d₂ - d₁d₃ - d₂d₃ + d₁d₂d₃. This shows the "losses" from cross-products that simple addition ignores.

You can approach but never reach 100% off with percentage discounts alone. THE MATH: Each discount multiplies by a fraction less than 1. Three 50% discounts: 0.5 × 0.5 × 0.5 = 0.125 (pay 12.5% = 87.5% off, not 150%). Three 75% discounts: 0.25 × 0.25 × 0.25 = 0.0156 (pay 1.56% = 98.44% off, not 225%). EXAMPLES WITH THREE EQUAL DISCOUNTS: | Each Discount | You Pay | Total Off |. | 20% | 51.2% | 48.8% |. | 30% | 34.3% | 65.7% |. | 40% | 21.6% | 78.4% |. | 50% | 12.5% | 87.5% |. | 60% | 6.4% | 93.6% |. | 75% | 1.56% | 98.44% |. APPROACHING 100%: To get 99% off total, you'd need: Three equal discounts of ~78.5% each. Or: 90% + 90% + (any amount) gets you 99%+. But mathematically, you'll never exactly reach 100% with percentage discounts. REALISTIC MAXIMUMS: Most aggressive real-world stack: Employee (20%) + Clearance (50%) + Coupon (20%) + Card (5%). = 1 - (0.80)(0.50)(0.80)(0.95). = 1 - 0.304 = 69.6% off.

For pure percentage discounts, the order does NOT matter mathematically. The final price is identical regardless of order. MATHEMATICAL PROOF: Multiplication is commutative and associative. 20% then 15% then 10%: $100 × 0.80 × 0.85 × 0.90 = $61.20. 10% then 20% then 15%: $100 × 0.90 × 0.80 × 0.85 = $61.20. 15% then 10% then 20%: $100 × 0.85 × 0.90 × 0.80 = $61.20. All paths lead to the same final price! WHY IT SEEMS LIKE ORDER MATTERS: The intermediate prices differ. 20% first: $100 → $80 → $68 → $61.20. 10% first: $100 → $90 → $72 → $61.20. The dollar amounts saved at each step differ. But the final total savings are identical. WHEN ORDER ACTUALLY MATTERS: 1. Rounding: If prices round after each discount. Different order → Different rounding → Pennies difference. 2. Conditional discounts: "Extra 10% if subtotal under $75". Order could affect qualification. 3. Caps or limits: "Max $50 savings per discount". Order matters when hitting caps. 4. Fixed-amount discounts mixed with percentage: "$20 off" then "10% off" ≠ "10% off" then "$20 off". PRACTICAL TIP: For pure percentages, don't worry about order. For complex deals with conditions or caps, test both orders.

Retailers strategically layer discounts to create excitement and perceived value. COMMON TRIPLE-DISCOUNT SCENARIOS: 1. Black Friday Super Stack: Base sale (40% off) + Coupon code (20% off) + App-exclusive (extra 10%). Sounds like: "Up to 70% off!". Reality: 56.8% off maximum. 2. Clearance Triple Markdown: Original markdown (30%) + Additional clearance (30%) + Final price cut (20%). Sounds like: "80% off original price!". Reality: 60.8% off. 3. Loyalty Program Stack: Member price (15%) + Points redemption (10%) + Birthday bonus (5%). Sounds like: "30% member savings!". Reality: 27.3% off. 4. Employee Purchase Day: Employee discount (20%) + Store sale (40%) + Friends & Family (15%). Sounds like: "75% off everything!". Reality: 59.2% off. WHY RETAILERS USE THIS STRATEGY: Psychological impact: Three discounts feel bigger than one. Engagement: Multiple codes/offers increase interaction. Price discrimination: Different customers stack differently. Clearance urgency: "Triple markdown" suggests final chance. MARKETING LANGUAGE TO WATCH: "Up to X% off" - Maximum possible, rarely achieved. "Take an EXTRA X%" - Applied to already-reduced price. "Stack your savings" - Implies more than actual discount. "Three ways to save" - Sounds like addition, it's multiplication. CONSUMER STRATEGY: Always calculate equivalent single discount. Compare to competitors' single offers. Check if all discounts can actually be combined. Read terms: "Cannot be combined" is common.

To compare, calculate the equivalent single discount for the triple stack. CALCULATION METHOD: Equivalent = 1 - (1 - d₁)(1 - d₂)(1 - d₃). EXAMPLE COMPARISON: Store A offers: 30% + 20% + 10% (stacked). Store B offers: 50% off (single). Store A equivalent: 1 - (0.70)(0.80)(0.90) = 49.6%. Store B: 50%. Store B is slightly better! QUICK REFERENCE FOR COMMON STACKS: | Triple Discounts | Equivalent | Compare To |. | 10% + 10% + 10% | 27.1% | 25-30% single |. | 20% + 15% + 10% | 38.8% | 35-40% single |. | 30% + 20% + 10% | 49.6% | 50% single |. | 40% + 20% + 10% | 56.8% | 55-60% single |. | 40% + 30% + 20% | 66.4% | 65-70% single |. FACTORS BEYOND PERCENTAGE: Additional perks: Triple stacks may include free shipping, gifts. Coupon restrictions: Single discount may have more exclusions. Points/rewards: Stacking might earn more loyalty points. Price matching: Easier with single-discount stores. DECISION FRAMEWORK: 1. Calculate equivalent discount for stack. 2. Compare to single discount offers. 3. Factor in additional terms and benefits. 4. Choose the better overall value. WATCH FOR: "Extra" discounts that exclude sale items. Minimum purchase requirements per discount. Expiration dates on stackable coupons.

Yes! The same mathematical principle extends to any number of discounts. FORMULA FOR FOUR DISCOUNTS: Final Price = Original × (1 - d₁) × (1 - d₂) × (1 - d₃) × (1 - d₄). Equivalent = 1 - (1 - d₁)(1 - d₂)(1 - d₃)(1 - d₄). EXAMPLE WITH FOUR DISCOUNTS: Original: $100. Discounts: 20%, 15%, 10%, 5%. Calculation: $100 × 0.80 × 0.85 × 0.90 × 0.95 = $58.14. Equivalent: 1 - 0.5814 = 41.86% off. (Not 50% from simple addition!). DIMINISHING RETURNS: Each additional discount has less absolute impact. | Added Discount | Price After | Incremental Save |. | 1st (20%) | $80.00 | $20.00 |. | 2nd (15%) | $68.00 | $12.00 |. | 3rd (10%) | $61.20 | $6.80 |. | 4th (5%) | $58.14 | $3.06 |. The 5% fourth discount saves only $3.06, not $5. GENERAL FORMULA: For n discounts: Final = Original × (1-d₁)(1-d₂)...(1-dₙ). Equivalent = 1 - ∏(1-dᵢ) for i = 1 to n. PRACTICAL LIMITS: Most retailers limit stacking to 2-3 discounts. Check "cannot be combined" terms. System limits may prevent excessive stacking. THIS CALCULATOR: Use our "Add fourth discount" option to calculate 4-way stacks!

Different industries have typical stacking patterns. RETAIL CLOTHING: Sale markdown (30-50%) + Coupon (15-20%) + Loyalty/Card (5-10%). Typical total: 45-65% equivalent. Peak times: Black Friday, end of season. ELECTRONICS: Holiday sale (10-20%) + Manufacturer rebate (5-15%) + Store card bonus (5%). Typical total: 18-35% equivalent. Note: Lower discounts but higher-value items. GROCERY/PHARMACY: Store sale price + Manufacturer coupon + Store coupon (sometimes). Typical total: 20-40% equivalent. Some stores allow double/triple coupon stacking. TRAVEL: Hotel sale rate (20-30%) + Member discount (10-15%) + Promo code (5-10%). Airline: Rare true percentage stacking. Car rental: Common triple stacks possible. FURNITURE: Store-wide sale (20-40%) + Room package bonus (10-15%) + Financing incentive (5-10%). Typical total: 30-55% equivalent. Often during holiday weekends. BEAUTY/COSMETICS: Brand promotion (15-25%) + GWP (gift with purchase) + Points multiplier. Harder to calculate due to gift values. Sephora/Ulta: Frequent stacking opportunities. RESTAURANT/FOOD: App discount (10-15%) + Promo code (10-20%) + Rewards (5-10%). Typical total: 22-38% equivalent. Most common in delivery apps. COMPARISON CHART BY INDUSTRY: | Industry | Typical Stack | Equivalent Range |. | Fashion | 30+20+10 | 45-55% |. | Electronics | 15+10+5 | 27-32% |. | Travel | 25+12+8 | 38-42% |. | Furniture | 35+15+10 | 50-55% |. | Food/Delivery | 15+15+10 | 35-38% |.