> For the complete documentation index, see [llms.txt](https://www.analytics-docs.laplacetec.com/guide/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://www.analytics-docs.laplacetec.com/guide/en/dashboard/formula.md).
# Understanding formulas
{% hint style="info" %}
**% display:** Measures calculated as ratios (repurchase rate, expected churn rate, margin rate, contribution margin rate, CTR, etc.) are shown with **%** in tables ยท tooltips ยท chart axes on the dashboard and custom dashboards. Decimals are shown up to two places, without trailing zeros (e.g., 72.3%, 33.52%). "X 100" in the formulas below refers to this % value.
{% endhint %}
## ๐ Revenue criteria used in practice
| Item | Meaning | Why it matters |
| ------------------------------- | -------------------------------------------------------- | ------------------------------------------------------ |
| VAT included/excluded | Whether to include VAT | Critical for settlement and profitability calculations |
| Reward points included/excluded | Whether to count points spent by consumers as revenue | Differs from actual cash flow |
| Claim calculation basis | When to deduct refunds/cancellations | Varies by performance evaluation/accounting method |
| Payment date+0 | Same-day payments - same-day claims | Most commonly used for daily performance analysis |
| Sales performance | Deducts claims from revenue by payment date | Used to calculate KPI/compensation performance |
| Accounting performance | Revenue by payment date - claims deducted by refund date | Basis for financial reporting and P\&L analysis |
When teams or companies interpret 'revenue' by different criteria, **serious problems can arise** in e-commerce operations. Because revenue figures serve as a key metric for many departments: in **performance evaluation, marketing decisions, financial reporting, and strategy planning**: **inconsistent criteria can undermine judgment and execution across the whole organization.**
So the first step in revenue analysis is **'clearly defining the criteria'**. You need to be able to **flexibly separate those criteria by team purpose or fix them at the system level**, and you need **an analytics tool that can automate the whole process**.
๐ The platform that meets all these requirements is **Laplace Analytics**.\
From defining practical revenue criteria to contribution margin analysis and claim handling settings, Laplace **provides a revenue analysis environment optimized for real e-commerce operations.**
## Order data
{% hint style="info" %}
**There is no measure called 'Gross revenue' or 'Total payments'.** The amount before deducting refunds/cancellations is the **Payment amount**, and the amount after deducting them is the measure \*\*Payment amount (excluding refunds/cancellations incurred)\*\*, which is shown as **Net sales** on some screens. If you see names like 'Gross revenue' or 'Total payments' on a dashboard, they're names given to a chart title or custom formula, so check which measure is actually used in the chart settings.
{% endhint %}
| Measure | Formula |
| ----------------------------------------------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| Payment amount | (Product price + Option price) x Quantity - Coupons - Discounts + Shipping fee |
| Actual Sales | Payment amount - Reward points - Deposits |
| Net sales | Payment amount - Refund/cancellation amount incurred |
| Gross merchandise value (GMV) | (Product price + Option price) X Quantity sold |
| Average order value (AOV) | Payment amount / Number of payments |
| ARPPU | Payment amount / Payment User Number |
| Basket size | Number of product options in one order number (if options A x1, B x2, C x3 are paid for at once, the basket size is 3 and the quantity sold is 6) |
| Average basket size | Basket size / Number of payments |
| Cohort LTV | Cumulative contribution margin / Cohort users |
| Cohort LTR | Cumulative payment amount / Cohort users |
| Cohort repurchase rate | Repurchase users / Cohort users X 100 |
| First-purchase promotion product recommendation | Average repurchase rate by first-purchase product = repurchase rate after a first purchase of product A, including purchases of all products such as A, B, C |
| Expected LTV | ARPPU X Expected retention period |
| Expected retention period | Paying users N periods ago / Expected churned users (= 100 / Expected churn rate (%)) |
| Expected churn rate | Users who paid N periods ago and haven't repurchased since / Paying users N periods ago X 100 |
| Paying-user growth capacity | First-purchase users X Expected retention period |
| Repurchase cycle | Median of each customer's (Last purchase date - First purchase date) / (Number of payments - 1) (for customers with 2 or more purchases) |
| Cross-selling | - When product A and product B are paid for under the same order number, it counts as cross-selling.
- Combinations of product A and product B are calculated per store.
- Only orders with 2 or more product options are counted.
- Refunded / canceled orders are included in the calculation.
|
| First/Repurchase | - Each customer's orders are counted in payment order, based on all orders regardless of the query period.
- First purchase : The customer's first order
- Repurchase : The customer's second and later orders
- Refunded / canceled orders are not counted by default.
|
## Ad data
| Measure | Formula |
| ----------------------- | ----------------------------------------------- |
| Ad spend per revenue | Ad spend / Payment amount (excl. VAT) |
| ROAS | Payment amount (excl. VAT) / Ad spend x 100 |
| Conversion ROAS | Conversion revenue (excl. VAT) / Ad spend x 100 |
| First Purchase CAC | Ad spend / Number of first-purchase payments |
| First-purchase user CAC | Ad spend / First-purchase users |
| Registration CAC | Ad spend / Number of sign-ups |
| Payment CAC | Ad spend / Number of payments |
| CPA | Ad spend / Conversions |
| CTR | Clicks / Impressions x 100 |
| CPM | Ad spend x 1000 / Impressions |
| Impression CVR | Conversions / Impressions x 100 |
| Click CVR | Conversions / Clicks x 100 |
## Base product data
| Measure | Formula |
| ------------------------ | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| Gross margin | Gross margin (incl. VAT) - Gross margin VAT
Gross margin (incl. VAT) = Payment amount - Cost
Gross margin VAT = Gross margin (incl. VAT) X 0.1 / 1.1
|
| Gross margin ratio | Gross margin / Payment amount (excl. VAT) X 100 |
| Contribution margin | Contribution margin (incl. VAT) - Contribution margin VAT
Contribution margin (incl. VAT) = Payment amount - Cost - Ad spend - Fees - Seller-paid shipping
Contribution margin VAT = Contribution margin (incl. VAT) X 0.1 / 1.1
|
| Contribution margin rate | Contribution margin / Payment amount (excl. VAT) X 100 |
| COGS rate | Cost (excl. VAT) / Payment amount (excl. VAT) X 100 |
| POAS | Actual gross margin / Ad spend X 100 |
| BEP ROAS | Actual Sales (excl. VAT) / Actual gross margin X 100 |
| ACoS | Ad spend / Conversion revenue (excl. VAT) X 100 |
## Request help from your dedicated manager
Have more questions about formulas?
Contact us through the inquiry page below or by email. Your dedicated manager will help you.
> ๐ฌ [Contact us on our website](https://www.analytics.laplacetec.com/contact)
**Email:** [**product@laplacetec.com**](mailto:product@laplacetec.com)