The Mathematics of Marketing: Ten Useful Formulas

The Mathematics of Marketing: Ten Useful Formulas

If you’ve been in a marketing role for any amount of time, you’ve likely heard “marketing” defined as both art and science.

This is generally true if we’re defining science as “systematized knowledge” or “the state of knowing” and art as the practical application of creativity, but I think that definition is missing another, equally important element: math.

Over the years, I’ve come to see marketing as the art, science, and math of making people feel and act. In campaigns and strategies that are truly effective, which is to say, when campaigns achieve the goal they set out to achieve, it’s because each one these disciplines—art, science, mathematics— have been attended to.

To the extent that it can be, nothing is left to chance.

As a writer, I’d much rather work with idioms than integers, but as a writer who works as a marketer, I’m not afforded that luxury. And right now, it seems, numbers are more important than ever.

So in an effort to showcase some of the math I’ve found helpful over the years, here are ten useful formulas to calculate the numbers you’re sure to use and encounter time and time again.


Churn Rate

Formula: % = (Customers Lost during the Period / Total Customers at the Start of the Period) × 100

The churn rate formula is calculated by dividing the number of customers lost during a certain time period by the total number of customers at the start of that period. The result is typically expressed as a percentage.

Essentially, the churn rate calculates the speed at which customers are leaving your service or unsubscribing.

It’s critical to understand if you’re losing customers at a rate that could threaten your business’s long-term profitability.

It’s also a lagging indicator that can help you understand if something is going wrong so you can course correct prior to it becoming a major issue in your business.


Cost per Acquisition (CPA)

Formula: CPA = Total Cost of Campaign / Number of Conversions

CPA measures the cost to acquire a new customer. It helps you evaluate the efficiency of your marketing campaigns by revealing the cost for each new customer gained through your marketing efforts.

It’s also incredibly useful to have when allocating your budget, setting pricing, and determining the feasibility of a long-term campaign.


Market Penetration Rate

Formula: % = (Number of Customers Who Purchased Your Product / Total Number of Potential Customers) × 100

Market penetration is calculated by dividing the number of customers who have purchased your product by the total number of potential customers in the market, and then multiplying the result by 100 to get a percentage.

This metric is typically used to gauge the reach of your marketing efforts, showing the percentage of potential customers who have actually purchased compared to the total market size.

You generally want this number to increase over time.


Market Share

Formula: (%) = (Company’s Sales / Total Market Sales) × 100

Market share is calculated by taking the sales figures of your company (usually in units sold or revenue) and dividing them by the total sales figures of the market (again, in units or revenue), then multiplying by 100 to get a percentage.

By comparing your sales volume to the total sales within your industry, market share indicates the extent of your control over the market.


Net Promoter Score (NPS)

Net Promoter Score (NPS) is calculated using customer feedback collected through a survey that asks respondents to rate the likelihood that they would recommend a company, product, or service to a friend or colleague. The rating is usually on a scale from 0 to 10.

Since this one is a bit more involved, here’s how you calculate NPS:

Categorize the Responses:

  • Promoters: Respondents giving a score of 9 or 10 are considered Promoters.
  • Passives: Respondents giving a score of 7 or 8 are considered Passives (and are left out of the calculation).
  • Detractors: Respondents giving a score between 0 and 6 are considered Detractors.

Calculate the Percentage of Promoters and Detractors:

  • Percentage of Promoters: (Number of Promoters / Total Number of Respondents) × 100
  • Percentage of Detractors: (Number of Detractors / Total Number of Respondents) × 100

Subtract the Percentage of Detractors from the Percentage of Promoters: This gives you the NPS, which can range from -100 (if every customer is a Detractor) to 100 (if every customer is a Promoter).

NPS = Percentage of Promoters – Percentage of Detractors


If you received responses from 100 customers, where 70 are Promoters and 10 are Detractors:

Percentage of Promoters = (70 / 100) × 100 = 70%
Percentage of Detractors = (10 / 100) × 100 = 10%

NPS = 70% – 10% = 60

This would result in an NPS of 60, which generally indicates a very healthy level of customer satisfaction and loyalty.

Remember that Passives are not factored into the final NPS calculation, although they represent a segment of customers whose loyalty is not assured.


Return on Ad Spend (ROAS)

Formula: Revenue from Ads / Cost of Ads

Return on Ad Spend (ROAS) is calculated by dividing the revenue generated from advertising by the cost of the advertising.

ROAS determines the monetary success of your advertising campaigns by comparing the revenue generated from ads to the cost of those ads.


Return on Investment (ROI)

Formula: (%) = ((Net Profit – Investment Cost) / Investment Cost) × 100

Return on Investment (ROI) is calculated by subtracting the initial investment cost from the net profit earned from the investment, then dividing that number by the initial investment cost, and finally multiplying by 100 to get a percentage.

ROI is a fundamental measure of the profitability of your investments. It shows the percentage of how much money has been made compared to the money invested.


Click Through Rate (CTR)

Formula: (%) = (Clicks / Impressions) × 100

Click-Through Rate (CTR) is calculated by dividing the number of clicks an advertisement or link receives by the number of times the advertisement or link is shown (impressions), then multiplying the result by 100 to convert it to a percentage.

CTR measures the effectiveness of your online advertisements by showing the percentage of viewers who click through to your website.


Conversion Rate

Formula: Conversion Rate (%) = (Number of Conversions / Total Number of Visitors) × 100

The conversion rate is calculated by dividing the number of conversions by the total number of visitors (or sessions, depending on the context) and then multiplying the result by 100 to express it as a percentage.

The conversion rate is a key performance indicator of your marketing effectiveness, showing the proportion of clicks that result in a desired action such as a sale or lead.


Cost Per Click (CPC)

Formula: CPC = Total Cost of Campaign / Total Number of Clicks

Cost Per Click (CPC) is calculated by dividing the total cost of your advertising campaign by the number of clicks received.

CPC gives you an average cost for each click on your ads, helping to manage and optimize your ad spend for various campaigns and keywords.

As you may have concluded, this is far from an exhaustive list, but knowing these numbers—and the formulas for how to arrive at them—is a great first step towards optimizing your efforts.

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