Rule of Three Calculator: Know If You’re Going To Hit Your Desired CPA

by | Feb 26, 2020

What is this calculator?

This calculator is a demonstration of the Rule of Three, which I covered in detail in my article, LumenMath: The Rule of Three, or Should I Keep This Audience or Platform Running?

It calculates how much you need to spend as well as how many impressions you need in order to be sure if a campaign will reach your desired CPA. In other words, a rough idea of at what point you’ll know if you’re still on track.


When to use this calculator:

This calculator is generally best used before you launch a campaign or shortly thereafter. The reason for this is because it works best for people who lack one of two things:

1. The context of campaign performance.
2. Prerequisite expertise to have a rough idea already of how performance will go.

In short, if you are an expert or have hired experts, trust that expertise over what this calculator says. Also, if you have context this calculator can’t take into account, trust the findings that include that context.

This calculator operates in a vacuum. It’s a pure demonstration of the Rule of Three mathematical concept you can use to better understand how your CPA will unfold. Further, it only tells you things as they are right now, so as things develop your calculations may change.

My main point with my LumenMath series is that, when executing advertising campaigns, you need to either rely on your experience and past data or use proven math concepts (like the Rule of Three) to make better decisions faster. Alright, with that out of the way, here it is!

Rule of Three Calculator

Desired Cost Per Acquisition (CPA)
Example: 25

Confidence Percentage

Most users will want 95 (or .95 -- both work).


Number of Impressions Already Served

Example: 5,000

Amount You’ve Already Spent

Example: 5

How to use this calculator:

For the full context on how to use this calculator read my article. The gist is that it’s difficult to know whether or not a platform or audience is performing well early on in a campaign (i.e., when you lack context). 

This calculation will provide an estimate of how much you’ll need to spend before you can be sure the campaign will or will not reach your target.

What numbers do I need? 

1. First, you need your Desired Cost Per Acquisition (CPA)

This is what you would like to spend for each specified action you’re measuring in your campaign (e.g., per form-fill, per sale, per click). For more on CPA, read our article on CPM vs. CPC vs. CPA.

2. Second, you need a Confidence Percentage.

The “Rule of Three” states the probability of an event occurring after n observations without witnessing the event is bounded by 3/n with 95% confidence. In other words, without past data or context, you can predict a range in which your CPA can lie. 

So, you most likely want to keep this at 95 (or .95 – both work), unless you’re a stats wiz or your CPA is really high. But at that point you’re probably an expert who may not need this calculator.

3. Third, you can plug in the Number of Impressions Already Served and Amount You’ve Already Spent.

These are optional, but if you provide both (it won’t work without both), the calculator will also tell you how many impressions you’ll need to serve as well.

Is there more?

Yes! If you’d like to dive deeper into the world of math and metrics, read my second article LumenMath: How to Better Predict Campaign Performance. It takes you through the concept of confidence intervals and how to (you guessed it…) predict performance. 

A calculator for this one is on its way! Subscribe below for updates.

Questions? Comments?

Contact us if you notice any issues, have any questions or comments.

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