# Fundamental Retail Math Formulas

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These formulas will help you evaluate your sales and inventory utilization, so you stay on top of your merchandise planning. (Pro tip: Keep this page bookmarked so you can get a quick refresher whenever you need!) If you're unsure what some of these terms mean, check out our list of basic retail terms to know to refresh your knowledge.

## Sales Metrics

ADS = Net Sales \$ / Number of Transactions

The average dollar transaction during a period of time.

### Average per Week (APW)

APW = Gross Sales Units/ Number of Weeks

Number of units sold for an item over a specific period of time. APW is an indicator for the rate of sale (or velocity) of a particular item, and can be used to predict how much that item is going to sell in the near future.

### Average Order Value (AOV)

Also known as Average Transaction Value (ATV)

AOV = Net Sales / Number of Transactions

The average amount a customer spends on a transaction. This gives a good sense of the customers' appetite to spend per visit at your store or website.

### Average Unit Cost (AUC)

Sales AUC  = COGS / Units Sold
Inventory AUC = Inventory at Cost / Units OH

The average amount you've paid per unit of inventory.

### Average Unit Retail (AUR)

Sales AUR = Net Sales \$ / Units Sold
Inventory AUR = Retail Inventory / Units OH

The average selling price of an item.

### Cost of Goods Sold (COGS)

COGS = (BOP Inventory + Net Purchases + Cost of Labor + Materials and Supplies + Other Costs) - EOP Inventory

The cost of the inventory that was sold within a specified time period. This is typically the largest cost a retailer incurs, so it is really important that you track this closely. It typically comes from the accounting system.

### Markdown

Permanent reduction in the price of an item. If products are not moving as fast as expected by a retailer, a retailer would typically reduce the price of the product, i.e. mark them down, to make the products more appealing for the customers.

To learn more, check out this blog post that visualizes how markdowns are taken off of the ticket price to give the sale price.

### Discount

The reduction in price that is applied to a sale at the point of purchase. This is different than markdowns, since the price of the product hasn't been reduced permanently or for everyone, but a temporary or one-off discount has been applied. 20% off for a special promotion or an employee discount would fall under this category.

To learn more, check out this blog post that visualizes how discounts are taken off of the ticket price to give the sale price.

### Allowances

Allowances = Discount \$ + Markdown \$

Total reductions off of the Ticket Price or the MSRP in a transaction. This helps showcase how much reduction you had to take to incentivize a sale.

### Gross Sales

Also known as top-line or gross revenue.

The total proceeds of all the sales within a time period. This typically comes from the accounting system.

### Initial Markup (IMU)

IMU = Ticket Price - Cost of Goods Sold
IMU% = (Ticket Price - Cost of Goods Sold) / Ticket Price * 100

Initial Markup is the difference between the initial ticket price of an item and its cost for the retailer. For example, if the cost of manufacturing an item was \$20 and the product is initially priced at \$100, then the initial markup will be \$80.

The Initial Markup Percentage gives the same metric as a percentage of the ticket price. Going with the earlier example, the IMU% would be (\$100 - \$20) / \$100, i.e. 80%.

Typical IMU percentages vary drastically between different types of retailers. IMUs in vertically integrated apparel retailers are typically in the 80% ranges, whereas IMUs for general merchandise within Walmart stores can be in the range of 20-30%.

### Maintained Markup (MMU)

MMU = Ticket Price - Cost of Goods Sold - Allowances
MMU% = Maintained Markup / Ticket Price* 100

The difference between the cost of an item and the sale price. Products are often not sold at the ticket price, but rather at a marked-down price or with the discount, i.e. at the sale price. In this case, the maintained markup is a better way to judge the profitability of an item than the initial markup.

MMU is the profit you generate from an item after all markdowns and discounts have been accounted for. To learn more about MMU, check out this post on the difference between IMU and MMU.

### Markup % (MU%)

MU% = (Ticket Price - Cost of Goods Sold) / (Cost of Goods Sold)

This formula tells you how much the price was increased from the cost price to the selling price, as a percentage of the cost price. Different retailers and product categories have very different MU%. Where as retailers like Costco, have very nominal markups like 10% to 20%, i.e. almost selling at cost since they generate most of their profits based on memberships, MU% in apparel retail is typically 100%-150% in wholesale relationships and can be as high as 500% for vertically integrated retailers.

### Net Sales

Net Sales = Gross Sales - Returns \$

The amount of sales generated after removing returns from Gross Sales, which is net of Allowances.

### Return Rate %

Return Rate %= Return Units / Sales Units

Percentage of the Sales that were returned in a given time frame. Return rates in retail can vary significantly by product category. While return rates in Apparel can be as high as 20% to 30%, return rates in fast moving consumer goods and beauty are typically relatively low, less than 5%. Separately, return rates vary significantly depending on the channel of purchase. For fashion apparel, physical stores experienced a return rate of about 3%, compared with about 25% for online sales based on USPS stats.

### Sale Price

Sale Price = Ticket Price - Allowances

The price at which the product is ultimately sold at. This is the price of the sale after the markdowns and discounts have been applied on the original ticket price.

To learn more, check out this blog post that visualizes how markdowns and discounts are taken off of the ticket price to give the sale price.

### Ticket Price

The price at which the product is initially priced to be sold at. This typically refers to the price written on the product's label, hence the name ticket price.

To see how Ticket Price is calculated, check out this blog post that shows how IMU (Initial Markup) is added to COGS to give the ticket price.

### Units per Transaction (UPT)

Also known as average basket size.

UPT = Units Sales / Number of Transactions

Average number of units sold per transaction. This is an important metric to keep an eye on over time, and also while designing the cart and checkout experiences. This number will vary drastically over different categories and will be larger in general merchandise and groceries categories and smaller in larger ticket categories like home, fashion and electronics.

## Productivity Metrics

### Sell Through (ST)

ST% = Units Sold / BOP Units On Hand * 100

The percent of inventory sold in a given period time. Mostly commonly a week. This is an important metric to watch for products in seasonal categories, such as fashion and home. Typically, you will want to look of sell-through in two ways: full-price sell-through and overall sell-through. Full-price sell-through is the percentage of the goods that were sold at full-price (without markdown or promotion) and the overall sell-through is the percentage of the goods that were sold regardless of promotional strategies.

### Gross Margin

Gross Margin = Gross Sales - COGS
Gross Margin % = (Gross Sales - COGS) / Gross Sales * 100

The revenue you retain after accounting for the cost of your products.

### Gross Margin Return on Investment (GMROI)

GMROI = Gross Margin \$ / Average Inventory at Cost

The gross margin dollars returned for every dollar invested in inventory. This is used as a measure of productivity of a particular category or SKU, i.e. investment area and makes a great benchmark between product groups or even between companies.

## Growth Metrics

### Build

Build = Total Sales / Previous Total Sales

A measure of growth on any metric from one period to the other. It is typically used to factor in week-over-week or month-over-month changes

### Comparable Store Sales (Comps)

Comps = Total Sales / Previous Same Store Total Sales - 1 * 100

A comparison of sales for stores that have been open more than a year. This helps you keep track of growth or decline across stores between two periods. This is a very important metric to track the organic growth of a retailer in existing channels over time. This differs from overall sales growth in that new store or channel additions are not included in Comps.

To learn more, check out Toolio's Guide for Comparable Store Sales Reporting and Planning.

## Inventory Metrics

### Average Inventory

Average Inventory = (Sum or all BOP inventory + EOP Inventory of the last period) / Number of Periods Used

The average amount of inventory a retailer holds over time. This is calculated in cost, units, or retail value for any period of time. It is calculated by averaging the beginning of period cost over multiple periods.

### Beginning of Period Inventory (BOP)

The total inventory a retailer owns at the beginning of a period. Owned inventory will directly impact the sales you can expect to achieve, since you can't sell products you don't have. BOP Inventory can be calculated in units, costs, or retail dollars. When calculated in units, it's referred to as BOP Units, etc. If you choose to look at BOP on a monthly basis, the metric is called Beginning of Month Inventory and if you choose to look at BOP on a weekly basis, the metric is called Beginning of Week Inventory.

### End of Period Inventory (EOP)

EOP (Period 1) = BOP (Period 2)

The total inventory a retailer owns at the end of a period. The EOP of a period, equals the BOP of the next period, since the retailer's inventory carries over to the next period. EOP Inventory can be calculated in units, costs, or retail dollars. If you choose to look at EOP on a monthly basis, the metric is called End of Month Inventory and if you choose to look at EOP on a weekly basis, the metric is called End of Week Inventory.

### Fill Rate

Fill Rate = Number of Line Items Shipped / Number of Line Items Ordered
Fill Rate = Number of Orders Shipped / Total Number of Orders

Fill Rate quantifies the ability to fulfill customer orders. It looks at the ratio between the total number of lines (e.g. items) successfully fulfilled and number of lines ordered. This can also be calculated by looking at the ratio on the Order level, instead of the Line Item level.

Even though the above formula is to quantify customer-facing operations, the same metric can be useful for quantifying supplier purchase orders. Using the same measure, it is very useful to look at the % of Supplier Purchase Orders are fulfilled and use that to the estimate future receipts with higher certainty.

### Stock to Sales (S/S)

S/S = Inventory at BOP / Prior Week Sales

The number of weeks of inventory on hand. This is based on prior weeks' sales. This is one of the most important inventory metrics to look at and is generally calculated on a monthly basis. It shows how much inventory was needed to achieve the sales generated within the period. The higher this number is, the higher the inventory overhead for the business will be. Like most inventory metrics, this will be a category dependent metric and will be lower in fast moving categories (like consumables and groceries categories) and higher in discretionary categories like (home, fashion and electronics).

### Inventory Turn

Also known as Turn

Turn = Cost of Goods Sold / Average Inventory (Cost\$ or Units)

The number of times the average inventory is sold and replaced during a specific time period. This measures how fast you are able to move through your stock and gives a sense of inventory productivity. Turn is a metric that is closely followed at the top level, and it is important track it for individual categories. Some categories like fast moving consumer goods or groceries will have higher turn numbers compared to high ticket items.

### Weeks of Supply (WOS)

WOS = On-Hand Inventory Units / Average Weekly Unit Sales

The number of weeks a given amount of inventory will last at the current rate of sale. The WOS number you target will depend on many things, including product category and lead time. For example, for products with low lead times, retailers will want to target low weeks of supply, since they know that they can replenish products rapidly as needed. For products with high lead times, or those that you cannot replenish but still have a long season ahead, you will want to keep Weeks of Supply close to the number of sale weeks remaining for that product.

### Forward Weeks of Supply (FWOS)

FWOS = On-Hand Inventory Units / Forecasted Average Weekly Unit Sales

Whereas WOS looks at trailing average to calculate the available weeks of supply for a particular item, Forward Weeks of Supply (FWOS) looks at forward looking demand, i.e. forecast to calculate the available weeks of supply, hence it is a more accurate metric. For products with low seasonality, WOS and FWOS will not be very different. However, for products that follow seasonal patterns, say swimwear, WOS and FWOS will be very different, and where possible, it will be better to use forward looking weeks of supply.

## Feels like a lot to monitor?

That’s because it is. Toolio helps you crunch these numbers so you can save time, reduce errors, remove guesswork, and focus on the fun stuff. If you want to see how it works, request a demo of Toolio.When you’re working with billions of data points, it’s hard to know exactly how to use that information in order to offer your customers the right products, in the right place, at the right time, for the right price. That’s why we’ve created this list of the most important retail math formulas that you should constantly be monitoring.