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🏷️ Business Discount Calculator
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Discount Calculator

Calculate sale price, find original price, or stack multiple discounts

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Sale Price
$80.00
Original price$100.00
You save$20.00
Savings percentage20%
Price after tax$80.00
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Original Price
$100.00
Before 20% discount
Amount saved$20.00
Sale price$80.00
Savings verified20.0% off
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Final Price
$72.00
Original price$100.00
Total saved$28.00
Effective discount28%
Note: 20%+10% ≠ 30% (it's 28%)
Price After Each Discount

How to Calculate a Percentage Discount

Calculating a discount is one of the most practical everyday math skills — whether you're shopping a sale, building a pricing strategy for your business, or verifying that an advertised "deal" is actually a deal. The core formula is simple, but there are several important variations that trip people up.

The fundamental discount formula:

Sale Price = Original Price × (1 − Discount% ÷ 100)

Examples of how to calculate percent off:

  • 10% off $150: $150 × 0.90 = $135 (save $15)
  • 20% off $150: $150 × 0.80 = $120 (save $30)
  • 25% off $200: $200 × 0.75 = $150 (save $50)
  • 33% off $90: $90 × 0.67 = $60.30 (save $29.70)
  • 50% off $80: $80 × 0.50 = $40 (save $40)

To find the discount percentage when you know both prices: Discount% = ((Original − Sale) ÷ Original) × 100. If something went from $200 to $140: ((200 − 140) ÷ 200) × 100 = 30% off.

Stacked Discounts: Why 20% + 10% Does Not Equal 30% Off

This is one of the most commonly misunderstood concepts in discount math, and retailers sometimes use this confusion to make offers appear more generous than they are.

When two discounts are applied sequentially, the second discount applies to the already-reduced price — not the original. Let's work through the math:

  • Starting price: $100
  • After 20% off: $100 × 0.80 = $80
  • After additional 10% off: $80 × 0.90 = $72
  • Total savings: $100 − $72 = $28
  • Effective discount: 28% — not 30%

The formula for combined effective discount when applying two discounts d1 and d2:

Effective Discount = 1 − (1 − d1)(1 − d2) = 1 − (0.80 × 0.90) = 1 − 0.72 = 0.28 = 28%

For three discounts (20% + 10% + 5%): 1 − (0.80 × 0.90 × 0.95) = 1 − 0.684 = 31.6% effective discount.

The gap between the sum and the effective discount grows as the percentages get larger. Two 50% discounts = 75% effective discount, not 100%. This is why "buy one get one free" (which equals 50% off per item) followed by a "members-only extra 20% off" is not 70% off — it's effectively 60% off.

Reverse Discount: Finding the Original Price Before a Discount

One of the most practically useful calculations — and the one most people get wrong — is finding the original price when you only know the sale price and the discount percentage.

The correct formula: Original Price = Sale Price ÷ (1 − Discount% ÷ 100)

Example: An item is marked $75 with a tag that says "25% off." What was the original price?

Original = $75 ÷ (1 − 0.25) = $75 ÷ 0.75 = $100

The most common mistake is adding the percentage back to the sale price: $75 × 1.25 = $93.75 — this is wrong. You must divide by the complement fraction, not multiply by 1 + the original discount percentage. These operations are not inverses of each other.

How Retailers Use Discount Psychology

Understanding the math behind discounts also means understanding how retailers use pricing psychology to influence purchasing decisions. Key tactics to be aware of:

  • MSRP inflation: Manufacturers' suggested retail prices are often set artificially high so retailers can advertise large percentage discounts. A "50% off MSRP" deal may actually be the product's typical street price.
  • Anchoring: Showing the crossed-out "original" price alongside the sale price creates a perception of savings even when the item has always sold at that price.
  • Partial discounts: Advertising "up to 70% off" when only a few clearance items are discounted that deeply, while most items see 10–20% reductions.
  • Bundle discounts: "Buy 2, get 1 free" = 33% off per item when buying 3, not 50% off. Compare to individual item pricing before assuming value.

The best defense: compare the sale price to what the item actually sells for at other retailers, not just the claimed original price. Tools like price history trackers can reveal whether a "deal" represents a genuine reduction.

Frequently Asked Questions

How do I calculate the sale price after a discount? ▼
Use the formula: Sale Price = Original Price × (1 - Discount% / 100). For example, 20% off a $150 item: Sale Price = $150 × (1 - 0.20) = $150 × 0.80 = $120. You save $30, which is 20% of the original price. Alternatively, calculate the savings first: Savings = Original Price × Discount% / 100, then Sale Price = Original Price - Savings.
How do I find the original price before a discount? ▼
If you know the sale price and the discount percentage: Original Price = Sale Price ÷ (1 - Discount% / 100). Example: an item is $75 after a 25% discount → Original = $75 ÷ (1 - 0.25) = $75 ÷ 0.75 = $100. A common mistake is adding the percentage back ($75 × 1.25 = $93.75 — this is WRONG). You must divide by the remaining fraction, not multiply by 1 + the percentage.
Why doesn't a 20% + 10% discount equal 30% off? ▼
Because sequential discounts apply to the already-reduced price, not the original. Example: $100 item with 20% off = $80. Then 10% off the $80 = $8 saved → $72 final price. Total saved = $28, which is only 28% off — not 30%. The combined effective discount formula is: 1 - (1 - d1)(1 - d2) = 1 - (0.80 × 0.90) = 1 - 0.72 = 28%.
How do I calculate the percentage discount between two prices? ▼
Discount% = ((Original Price - Sale Price) ÷ Original Price) × 100. Example: original price $200, sale price $150 → Discount% = ((200 - 150) ÷ 200) × 100 = (50 ÷ 200) × 100 = 25%. This also works in reverse to verify a discount: if an item went from $200 to $150, that's a genuine 25% discount.
What is the formula for calculating discounts? ▼
Three key formulas: (1) Sale Price = Original × (1 - Discount%/100). (2) Original Price = Sale Price ÷ (1 - Discount%/100). (3) Discount% = (Savings ÷ Original) × 100. For stacked discounts: Final = Original × (1 - d1/100) × (1 - d2/100) × (1 - d3/100). Note that stacked discounts always result in a smaller total discount than the sum of the individual percentages.
How do I calculate a discount with sales tax? ▼
Always apply the discount first, then add tax. Formula: Final Price = Original Price × (1 - Discount%/100) × (1 + TaxRate%/100). Example: $100 item, 20% discount, 8% sales tax → Sale Price = $100 × 0.80 = $80 → With tax = $80 × 1.08 = $86.40. Never apply tax to the original price before discounting, as discounts typically apply to the pre-tax price.
What is a good discount percentage? ▼
For retailers, a 10–20% discount is considered a modest sale, while 30–50% off is a significant sale that strongly drives purchasing behavior. Discounts above 50% are often used for clearance, end-of-season sales, or to create urgency. For consumers, the key question is not the percentage but the actual savings relative to the real market price — retailers sometimes inflate 'original' prices (MSRP) before applying discounts to make the percentage appear larger.
How do stores calculate markdowns? ▼
Retailers use different markdown strategies: (1) Percentage markdown — reduce price by a fixed % (most common). (2) Dollar markdown — reduce by a fixed amount (e.g., $20 off). (3) BOGO (buy one get one) — effectively a 50% discount per item if identical items. (4) Tiered discounts — the more you buy, the higher the discount. The key insight for shoppers: compare the sale price to the actual market price (what competitors charge), not just the claimed original price, which may be an inflated MSRP that no one actually pays.
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