Discount Calculator

Work out the price after a percentage discount — or flip it to recover the original price when all you see is the discounted price.

How discount math works

Understanding discount math is essential for both consumers and sellers. For consumers, knowing how discounts work prevents the cognitive trap of "fake discounts" — a pricing tactic where a product is listed at an inflated "original" price before a discount that brings it back to its actual market value, creating an illusion of savings. For sellers, understanding discount stacking and the difference between markdowns and markups is fundamental to pricing strategy. The basic principle: to find a sale price, multiply the original price by one minus the discount as a decimal. To find the original price from a sale price, divide by one minus the discount as a decimal.

Discounts interact in ways that are counterintuitive. Two sequential discounts — say 20% off followed by an additional 15% off — do not equal 35% off total. The math is multiplicative: after the first 20% discount, the price is 80% of original. After the additional 15% off that reduced price, you pay 85% of 80%, which is 68% of original — a total effective discount of 32%, not 35%. This is a common marketing mistake where consumers and even some business owners overestimate the total savings. Compound discounts like this are one reason "buy one get one 50% off" deals are often less valuable than they appear.

Stacking discounts vs. single discounts

For a seller, applying a single 30% discount generates more sales than applying three sequential 10% discounts, even though the effective discount is identical. This is because the first 10% discount attracts some price-sensitive buyers, the second attracts more, and the third attracts even more — whereas a single 30% discount only attracts buyers who were willing to pay at least 70% of full price. This is why clearance sales often have a "additional 30% off already reduced items" tag: the first markdown attracted mid-season buyers, the additional discount attracts clearance shoppers who would not have bought at the first price.

For consumers, understanding stacking helps you evaluate whether a "deal" is genuine. A 50% off coupon applied to an already-reduced price is mathematically equivalent to a 75% off single discount — but merchants prefer presenting it as two separate steps because the intermediate "savings" feel larger. Always calculate the final price, not the cumulative percentage savings.

Frequently asked questions

How do I calculate a sale price from a discount?

Multiply the original price by one minus the discount as a decimal. Formula: Sale Price = Original × (1 − discount). For a 25% discount: multiply by 0.75. Example: $120 × 0.75 = $90 sale price. The key is converting the percentage to decimal form first — 25% becomes 0.25, and 1 − 0.25 = 0.75.

How do I find the original price from a discounted price?

Divide the sale price by one minus the discount as a decimal. Formula: Original = Sale Price ÷ (1 − discount). Example: $80 sale price at 20% off means $80 ÷ 0.80 = $100 original. This is the reverse discount formula and works for any discount percentage. This is also useful for verifying "was/now" pricing claims — if a retailer says something is "30% off" but the math does not produce a believable original price, the "discount" may be inflated.

Do sequential discounts add up or multiply?

They multiply, not add. Two 20% discounts: first takes price to 80% of original; second takes it to 80% × 80% = 64% of original, which is a 36% total discount, not 40%. Three 10% discounts: 0.90 × 0.90 × 0.90 = 0.729 = 27.1% total discount. This is a common source of confusion in marketing — "40% off plus an additional 20% off" sounds like 60% off but is actually 52% off. Always calculate the final price by multiplying the decimal factors sequentially.

What is the difference between markup and margin?

Markup and margin are two ways of expressing the same relationship between cost and selling price, but they are calculated differently and often confused. Margin is expressed as a percentage of the selling price: Margin = (Selling Price − Cost) ÷ Selling Price. Markup is expressed as a percentage of the cost: Markup = (Selling Price − Cost) ÷ Cost. A product that costs $60 and sells for $100 has a margin of 40% (40/100) and a markup of 67% (40/60). Retailers often think in markup terms; consumers and investors typically think in margin terms. Using the wrong calculation leads to significant pricing errors.

How do I calculate percentage change (increase or decrease)?

Percentage change = ((New Value − Old Value) ÷ Old Value) × 100. If a stock goes from $50 to $60, the increase is (60−50) ÷ 50 × 100 = +20%. If it drops from $50 to $40, the change is (40−50) ÷ 50 × 100 = −20%. The base of the calculation is always the original value, not the new value — this is why percentages of percentages compound differently than most people expect.

What is a "fake discount" and how do I spot one?

A fake discount is when a retailer raises the "original" price immediately before a sale, making the discount appear larger than the actual value reduction. This is also called "price anchoring" and is legal in most jurisdictions as long as the higher price was a genuine prior price. To spot fake discounts: check price history on websites like CamelCamelCamel (for Amazon) or Honey; look at how long the "sale" price has been active (a perpetual "sale" is not a sale); verify the math — if 40% off produces a price that is not meaningfully below market rate for comparable products, the discount may be inflated.

What is the original price formula for compounded discounts?

For multiple sequential discounts, the original price formula is: Original = Sale Price ÷ (1 − discount₁) × (1 − discount₂) × ... etc. For example, a sale price of $54 after a 20% off followed by a 30% off clearance: original = $54 ÷ 0.80 ÷ 0.70 = $54 ÷ 0.56 = $96.43 original. This is useful for verifying whether a clearance rack price represents genuine savings against the original retail price, or whether the pre-clearance price was already inflated.

Last updated Sep 7, 2026 — rates and figures change over time, so always confirm with the current source.

Figures are estimates for general information, not financial advice — see our disclaimer.

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