Retail math is the set of formulas retailers use to price goods, plan inventory, and measure sales performance — margin, markup, markdown, sell-through, turnover, GMROI, AUR, and similar calculations. Almost all of it reduces to a handful of ratios built from cost, retail price, units, and time, applied consistently across a buy, a season, or a store.

What is the IMU formula in retail?

Initial markup (IMU) = (retail price − cost) ÷ retail price, expressed as a percentage. A $100 retail item costing $40 has an IMU of ($100 − $40) ÷ $100 = 60%. IMU is planned before the season starts and is meant to cover markdowns, shrink, and operating costs while still leaving the target maintained margin.

What is the difference between markup on cost and margin on retail?

Markup on cost divides by cost; margin (markup on retail) divides by the retail price. A $40 cost item at $100 retail has 150% markup on cost ($60 ÷ $40) but 60% margin on retail ($60 ÷ $100). They describe the same $60 gross profit — always confirm which base a stated percentage uses before comparing numbers.

What is a retail math cheat sheet supposed to cover?

A useful cheat sheet covers three groups: pricing and margin math (cost, markup, IMU, keystone, maintained margin, markdown %), inventory math (turnover, GMROI, weeks of supply, sell-through, stock-to-sales), and sales performance math (AUR, UPT, ATV, conversion rate, sales per square foot) — each with the formula and one worked number, not just a name.

What is keystone pricing?

Keystone pricing sets retail price at double the wholesale cost — a 50% margin on retail, or 100% markup on cost. A $30 cost item keystones to $60 retail. It is a simple starting point rather than a strategy: categories with higher shrink, more markdowns, or higher service costs often need more than keystone to hit a target maintained margin.

How do you calculate maintained margin?

Maintained margin = (net sales − cost of goods sold) ÷ net sales, calculated after markdowns are taken, unlike IMU which is planned before them. If a style plans a 60% IMU but sells through with heavy markdowns, maintained margin will land below 60% — the gap is exactly the margin points given up to move the stock.

What is the retail formula for converting cost to a target margin price?

Retail price for a target margin = cost ÷ (1 − target margin %). A $40 cost item with a target 55% margin prices at $40 ÷ (1 − 0.55) = $40 ÷ 0.45 = $88.89. This is the formula to use when you know your cost and your required margin and need to solve for the retail price, rather than checking margin on an already-set price.

Retail math formulas: the full cheat sheet

Retail math is a short list of ratios reused everywhere: cost, retail, and time. This page groups every formula a buyer or planner actually uses — pricing and margin, inventory velocity, and sales performance — with the plain-text formula and a worked number for each.

Plan a markdown schedule What is a markdown in retail?

Pricing and margin math

Every pricing formula starts from the same two numbers — cost and retail price — and asks a different question of them: how much was added, what fraction of the price is profit, and what happens to that fraction after markdowns.

Pricing and margin formulas

Metric	Formula	Worked example	Result
Cost	What you pay the vendor per unit	—	$40.00
Retail price	The ticketed selling price	—	$100.00
Markup on cost	(Retail − cost) ÷ cost	($100 − $40) ÷ $40	150%
Margin on retail (IMU)	(Retail − cost) ÷ retail	($100 − $40) ÷ $100	60%
Keystone retail	2 × cost	2 × $40	$80.00
Maintained margin	(Net sales − COGS) ÷ net sales, after markdowns	($8,500 − $4,200) ÷ $8,500	50.6%
Markdown %	Markdown $ ÷ original retail $	$20 ÷ $100	20%
Markdown % of net sales	Total markdown $ ÷ total net sales $	$3,000 ÷ $15,000	20%

Cost / retail / margin / markup converter

Unit cost ($)

Retail price ($)

Target margin (%)

Gross profit per unit: $60.00
Margin on retail: 60.0%
Markup on cost: 150.0%
Keystone retail: $80.00
Retail needed for 55% margin: $88.89

Margin on retail and markup on cost describe the same gross profit dollar amount from two different bases — always check which one a stated percentage uses.

Inventory math

Inventory formulas measure how efficiently stock turns into sales — over a season (turnover, GMROI), at a point in time (weeks of supply), or as a running rate (sell-through, stock-to-sales, shrink).

Inventory and velocity formulas

Metric	Formula	Worked example	Result
Inventory turnover	Net sales (or COGS) ÷ average inventory	$400,000 ÷ $100,000	4.0x
GMROI	Gross margin $ ÷ average inventory cost	$180,000 ÷ $90,000	2.0x
Weeks of supply	Units on hand ÷ average weekly units sold	500 ÷ 50	10.0 wks
Sell-through rate	Units sold ÷ units received (or on hand), over a period	300 ÷ 500	60%
Stock-to-sales ratio	Beginning-of-month inventory $ ÷ that month's sales $	$60,000 ÷ $20,000	3.0
Shrink %	(Book inventory − physical inventory) ÷ net sales	$8,000 ÷ $400,000	2.0%

Sales performance math

These formulas describe what happens once a customer is in front of a register or a checkout page: how much they buy, how many units, and what fraction of traffic converts.

Sales performance formulas

Metric	Formula	Worked example	Result
Average unit retail (AUR)	Net sales $ ÷ units sold	$50,000 ÷ 2,000	$25.00
Units per transaction (UPT)	Units sold ÷ number of transactions	2,000 ÷ 800	2.5
Average transaction value (ATV)	Net sales $ ÷ number of transactions	$50,000 ÷ 800	$62.50
Conversion rate	Transactions ÷ traffic (visitors)	800 ÷ 5,000	16%
Sales per square foot	Net sales $ ÷ selling square footage	$500,000 ÷ 2,500 sq ft	$200

Deep dives

Which calculator do I need?

Each metric above has its own dedicated calculator with the full formula, worked examples, and an interactive tool.

Pricing a new item

Use: this page's converter, or Initial markup calculator

Solve cost ↔ retail ↔ margin ↔ markup, or plan the IMU an entire buy needs to carry.

Sizing a markdown

Use: Planned markdown calculator

Model price periods, sell-through per period, and the maintained margin the markdown schedule produces.

Checking maintained margin after the fact

Use: Maintained margin calculator

Compare planned IMU against what a season actually delivered once markdowns are booked.

Judging inventory speed

Use: Inventory turnover calculator

Net sales or COGS against average inventory, for a season or a full year.

Judging inventory profitability

Use: GMROI calculator

Gross margin dollars returned per dollar of average inventory cost — the profitability lens turnover misses.

Checking if stock will run out or sit too long

Use: Weeks of supply calculator

Units on hand against weekly sales pace, compared with the weeks actually left in the season.

Reading weekly velocity

Use: Sell-through rate calculator

Units sold against units available, the number that feeds directly into weeks of supply.

Deciding how much to buy next

Use: Open-to-buy calculator

Planned sales, planned ending stock, and on-order inventory netted into a dollar buying limit.

Averaging price across a range

Use: Average unit retail calculator

Net sales divided by units sold, the metric that tracks whether markdowns are dragging the average price down.

Keep planning

Initial markup calculator
Plan the IMU a full buy needs to cover markdowns, shrink, and target maintained margin.
GMROI calculator
Gross margin return on inventory investment, the profitability half of the turnover story.
Inventory turnover calculator
Net sales or COGS against average inventory.
Sell-through rate calculator
Weekly and cumulative sell-through, the velocity number behind most markdown decisions.

Answers

Retail math questions

Turn the formulas into a full season plan

Enter your assortment once and see IMU, sell-through, and maintained margin flow through an actual markdown schedule instead of a single static number.

Free, no sign-up, with CSV export and a shareable link. Pro ($29/mo) saves named season plans, imports inventory CSVs, and prints a decision memo.

Open the markdown planner