Math Solutions

Ad Campaign Metrics Calculator Calculator

Resolve paid acquisition economics. Precise engine for evaluating CPM, CTR, CPC, and ROAS across Facebook, Google, and algorithmic traffic networks.

Problem Parameters
Traffic Sourcing & Burn
$
Click-Through & Conversion Math
$

Total dollar amount of sales directly attributed to the ads.

Cost Per Mille (CPM / 1000 Views): $ 10.00
Click-Through Rate (CTR): 2.00%
Cost Per Click (CPC): $ 0.50
Cost Per Acquisition (CPA): $ 20.00
Return on Ad Spend (ROAS): 250%
PROFITABLE CAMPAIGN: A ROAS of 250% means every $1.00 you feed the advertising algorithm returns you $2.50 in gross revenue. Scale campaign budget.
Solution
Campaign ROAS (Return on Ad Spend)
250%
Bidding
Spend Model
Attribution
Yield Math

Digital Marketing Equations

From CPM to ROAS, learn the fundamental mathematics that separate bankrupt startups from viral ecommerce titans on the Facebook Ads and Google Ads networks.

The Advertising Funnel Physics

Digital advertising is entirely algorithmic. You buy attention (Impressions), convert that attention into action (Clicks), and manipulate those actions into sales (Conversions). Your success requires maintaining strict mathematical ratios down the entire funnel.

Standard Metrics

  • CPM (Cost Per Mille): The dollar amount it costs to show your ad to 1,000 distinct people. (e.g., $10 CPM). This tests whether your audience targeting is cheap or fiercely competitive.
  • CTR (Click-Through Rate): If 100 people see your ad and 2 click it, your CTR is `2.0%`. This mathematically tests if your ad creative (image/video) is compelling.
  • CPC (Cost Per Click): Exactly how much money you pay Mark Zuckerberg every time a user taps your advertisement.
  • CPA (Cost Per Acquisition): The cost to generate an actual paying customer (e.g., $20 CPA means you spent $20 on average for every 1 sale generated from clicks).

Return on Ad Spend (ROAS)

ROAS is the ultimate heartbeat metric of an ecommerce brand. If your ROAS is `100%`, it means you spent $1,000 and the ads generated exactly $1,000 in sales. Mathematically, because you have to pay to manufacture the product itself, a `100%` ROAS means you are losing massive amounts of money.

Most ecommerce brands require a minimum ROAS of `200%` just to hit break-even profitability. Anything over `300%` is incredibly lucrative and warrants immediately doubling your advertising budget.