A markdown in math is a reduction from a product’s regular selling price, resulting in a lower “sale price.” It’s one of the core concepts in business mathematics, sitting alongside markup and discount as the building blocks of retail pricing. While the idea is simple (the store lowers its price), the math behind it involves specific formulas for calculating how much the price drops, what the new price is, and what percentage the reduction represents.
Markdown vs. Discount
Markdown and discount both describe a price reduction, but they come from different perspectives. A discount is the reduction as the customer sees it. A markdown is that same reduction from the retailer’s point of view. In a math class, the distinction matters because the starting price in each calculation may differ. A discount typically comes off a manufacturer’s list price, while a markdown comes off the store’s regular selling price.
The Three Core Formulas
Markdown math revolves around three calculations: the sale price, the markdown amount in dollars, and the markdown rate as a percentage. Each one uses slightly different inputs, but they all start from the same place: the original selling price.
Sale Price
To find the sale price, multiply the original selling price by one minus the markdown rate (expressed as a decimal). The formula looks like this:
Sale Price = Selling Price × (1 − Markdown Rate)
For example, if a store marks down a $39.99 item by 10%, the sale price is $39.99 × (1 − 0.10) = $35.99.
Markdown Amount in Dollars
You can find the dollar amount of the markdown in two ways, depending on what information you have:
- If you know the markdown rate: Markdown Amount = Selling Price × Markdown Rate. Using the same example: $39.99 × 0.10 = $4.00.
- If you know both prices: Markdown Amount = Selling Price − Sale Price. So $39.99 − $35.99 = $4.00.
Markdown Rate (Percentage)
When a store advertises a markdown as a percentage, that number comes from dividing the markdown amount by the original selling price, then multiplying by 100:
Markdown Rate = (Markdown Amount ÷ Selling Price) × 100
If a product originally selling for $877.50 is reduced by $100, the markdown rate is ($100 ÷ $877.50) × 100 = about 11.4%.
A Step-by-Step Example
Suppose a clothing store sells a jacket for $120 and wants to clear it out with a 25% markdown.
First, find the markdown amount: $120 × 0.25 = $30. The jacket’s price is being reduced by $30.
Next, find the sale price: $120 − $30 = $90. Or use the single-step formula: $120 × (1 − 0.25) = $90.
Now imagine the problem works in reverse. You see a jacket on sale for $90 that originally sold for $120, and your textbook asks for the markdown rate. Subtract to find the dollar markdown ($120 − $90 = $30), then divide by the original price: ($30 ÷ $120) × 100 = 25%.
Why Businesses Use Markdowns
Understanding the “why” helps with word problems, because your textbook will often frame markdown questions around real business scenarios. Markdowns typically happen for four reasons:
- Clearing excess inventory: A store ordered too much and needs shelf space for new products.
- Removing damaged or discontinued items: Products that can’t be restocked at full price.
- Boosting sales volume: Lower prices attract more buyers, increasing total revenue even if profit per item drops.
- Encouraging add-on purchases: A marked-down item draws customers in, and they buy other full-price products while shopping.
Retailers also time markdowns around seasonal events. Inventory that hasn’t sold as a season winds down typically gets marked down more aggressively. A useful rule of thumb in retail math: when a store’s inventory level stays high relative to its sales for several months in a row, deeper markdowns follow.
Markdown Cancellation
Some math courses also cover markdown cancellation. This is what happens when a sale ends and the store raises the price back to the original selling price. The cancellation doesn’t create a new, higher price; it simply reverses the temporary reduction. In calculation terms, the markdown cancellation amount equals the difference between the sale price and the restored selling price, which is the same as the original markdown amount if the price goes all the way back up.
Common Mistakes to Avoid
The most frequent error in markdown problems is confusing the selling price with the cost price. A markdown always starts from the selling price (what the customer would normally pay), not from what the store paid for the item. If a problem gives you the store’s cost and asks for a markdown, you first need to calculate the regular selling price using markup formulas, then apply the markdown to that number.
Another common slip is forgetting to convert percentages to decimals before multiplying. A 15% markdown means you multiply by 0.15, not 15. And when you’re finding the sale price in one step using the (1 − d) formula, make sure you subtract the rate from 1 first. A 15% markdown means you multiply the selling price by 0.85, not 0.15. Multiplying by the rate alone gives you the dollar amount of the reduction, not the new price.