Markdown Calculator

Markdown, discount, clearance: the words stores use

A markdown is a price cut a retailer takes on its own merchandise. The store bought the goods, put them on the floor at $79.99, and later decided the price had to come down. When the ticket drops to $59.99, the $20.00 difference is the markdown and 25% is the markdown percent. No coupon, no competitor match, no member deal: the store is repricing its own inventory.

The formula is short. Markdown percent = (original price minus sale price) divided by original price, times 100. With those numbers: (79.99 - 59.99) / 79.99 = 0.2500, so 25%. Run it the other way and sale price = original price x (1 - markdown percent / 100), so 79.99 x 0.75 = 59.99.

People use the word loosely, so a note on scope. A discount is any reduction a shopper receives, coupons and promotions included. A markdown is the retailer's own decision to lower the shelf price, which is the number a buyer or shop owner tracks. Clearance is a markdown taken to empty a shelf, usually the deepest cut of the season. This page does markdown math in the retail sense, and it has nothing to do with the text formatting language that happens to share the name.

The two directions this calculator works in

The first direction is the one on the tag: you know the original price and the markdown percent, and you want the new price. Take 25% off $79.99. Convert the percent to a multiplier by subtracting it from 100, so 100 - 25 = 75, then multiply: 79.99 x 0.75 = 59.99. The dollars off are 79.99 - 59.99 = 20.00.

The second direction is the one people need after the fact: you know two prices and want the percent. A jacket that was $80 is now $60. The dollars off are 20, and the percent is 20 / 80 = 0.25, or 25%. The base matters here. Twenty dollars off an $80 item is 25%, but the same twenty dollars off a $50 item is 40%, because you divide by a smaller original price.

The calculator runs both at once, in separate rows, so you can check a tag and check a receipt without retyping. It also takes an optional second markdown, which is the subject of a later section, because two cuts in a row do not add up the way most people expect.

A 25% markdown on $79.99, step by step

Start with the original price of $79.99 and the markdown of 25%. The multiplier is 0.75. Multiply: 79.99 x 0.75 = 59.9925. That is not a price anyone can charge, so it rounds to $59.99. The markdown dollars are 79.99 x 0.25 = 19.9975, which rounds to $20.00. The tag can say "25% off" or "$20.00 off" and both describe the same cut, because the half cent disappears in the rounding.

The same arithmetic on other common markdowns gives the ladder below. Each row is 79.99 multiplied by one minus the percent, then rounded to the nearest cent.

Notice how the dollars off grow faster than the percent looks. The jump from 25% to 40% is 15 percentage points, but it moves the price from $59.99 to $47.99, a further $12.00, which is 20% of the already reduced price. Retailers feel that difference in the margin, which is why 40% is usually a seasonal decision and 25% is a mid-season one.

Stacked markdowns: the second cut lands on a smaller price

Two markdowns in a row do not add. Take 25% off $79.99, then take another 20% off what is left. The first cut gives $59.99. The second cut applies to $59.99, not to $79.99: 59.99 x 0.80 = 47.99. The total reduction is 79.99 - 47.99 = 32.00, which is 40.0% of the original ticket, not 45%.

The shortcut is to multiply the multipliers. 0.75 x 0.80 = 0.60, so the shopper pays 60% of the original price and the combined markdown is 40%. Any number of cuts can be chained this way, and the combined percent is always smaller than the sum of the percentages, because each later cut is computed on a base that has already shrunk.

The third row is the one that surprises people. A 20% markdown followed by a 25% markdown lands on the same place as 25% followed by 20%, because multiplication does not care about order: 0.80 x 0.75 and 0.75 x 0.80 both equal 0.60. If a store advertises "an extra 25% off already reduced items", that is a stacked markdown, and the honest total is 40%, not 45%.

Markdown, discount, clearance and coupon side by side

Four words, four different things, and the math is the same only for the first two. A markdown changes the shelf price for everyone. A discount is the general term for any reduction, including the ones a shopper sets off. Clearance is a markdown with a purpose, which is to get the last units out of the building. A coupon is a reduction the shopper brings to the register, and it usually does not change the shelf price at all.

For a shopper the distinction matters when you stack things. A 30% clearance markdown plus a 10% store coupon is not 40% off; it is 0.70 x 0.90 = 0.63, so 37% off, and the coupon comes off the clearance price. For a shop owner the distinction matters in reporting, because markdown dollars are money given up on inventory you already own, while coupon redemptions are usually a marketing expense.

One more term that shows up on tags: the "was" price. If a tag reads "was $79.99, now $59.99", the markdown percent is 25% only if $79.99 was a price the item had sold at. The FTC Guides Against Deceptive Pricing (16 CFR 233.1) treat a former price as legitimate when it was offered on a regular basis for a substantial period, and not when it was invented to make a sale look deeper. That is a rule about advertising, not about arithmetic, and the FTC advertising FAQ for small business says the same in plainer words.

Markdown dollars and the average markdown percent

Shops do not track markdowns one tag at a time. They track markdown dollars, which is the price given up multiplied by the units sold at that price, and then compare that total to the original retail value of the goods. The table below is a small end of season report for one style.

The original retail value is 10 x 79.99 + 5 x 49.99 = 799.90 + 249.95 = 1,049.85. Markdown dollars of 323.00 divided by 1,049.85 gives 30.8%, and that is the number to report. The average of the three percentages is (25 + 40 + 30) / 3 = 31.7%, which is close here but wrong in general, because it gives the same weight to 4 units as to 6. Weight by dollars and the answer is 30.8%.

That gap gets large when the mix is uneven. If 40 units sold at 10% and 2 units sold at 70%, the simple average is 40%, while the real markdown rate is closer to 13%. Buyers who report the simple average get asked hard questions at the end of a season, which is why the formula is always markdown dollars over original retail dollars.

What a markdown does to the margin

A markdown comes straight out of gross margin, because the cost of the goods does not move. Say an item costs the store $40.00 and sells at $79.99. Gross margin is (79.99 - 40.00) / 79.99 = 50.0%, and profit per unit is $39.99. Mark it down 25% and the price is $59.99, so margin falls to (59.99 - 40.00) / 59.99 = 33.3% and profit per unit is $19.99.

The unit volume needed to make up the difference is the part people underestimate. One unit at $79.99 earned $39.99. Two units at $59.99 earn 2 x 19.99 = $39.98, one cent short of what the single full price sale brought in. A 25% markdown therefore needs roughly double the units to hold the same gross profit dollars, and most seasonal goods do not double their sell through just because the price dropped a quarter.

That is the arithmetic behind the common retail habit of marking down late and deep rather than early and shallow. A 40% markdown on the same item leaves $7.99 of profit per unit, so it takes five units to match one full price sale. Deep cuts clear a shelf, but they rarely rebuild the dollars, which is why the decision is usually about cash and space rather than profit.

Rounding, sales tax and the mistakes that cost money

Half cents. Some markdowns land exactly between two cents. Half of $79.99 is 39.995, so a 50% tag can read $39.99 or $40.00 depending on how the store rounds. Either is defensible, but the tag and the register have to agree, and the markdown report should use the price the register charged.

Tax comes after the markdown. Sales tax is charged on the price you pay, not the original ticket. At 8% tax, a $59.99 sale price carries 59.99 x 0.08 = 4.80 in tax, for a total of 64.79. Charging tax on the original $79.99 would overcharge by 1.60, which is 8% of the $20.00 the shopper never paid.

Percent against percentage points. Moving from 25% off to 40% off is a 15 point change, not a 15% change. The markdown percent itself grew by 15 / 25 = 60%. Mixing the two produces sentences that sound right and are wrong, and they show up in ads, memos and news stories every sale season.

Round once. If you chain a markdown and a tax, do not round the intermediate price twice. 79.99 x 0.75 = 59.9925, and the register rounds to 59.99 once. Rounding to 60.00 first and then taking tax gives a different total by a cent or two, which is small per sale and large across a season. The calculator here keeps full precision and rounds only what it displays.

Check the base. A markdown percent is only meaningful next to the price it started from. "$20.00 off" is 25% on $79.99 and 40% on $49.99, so a report that lists dollars off without the original price cannot be compared across styles.