The hidden balance: How CPM and CTR shape real advertising costs 💵

At first glance, this seems obvious - higher CTR and lower CPM mean cheaper clicks. But beneath that simplicity lies a deeper structure. To see it clearly, let’s hold CTR constant for a moment and watch what happens when CPM moves.

If CTR is 2%, then 10 × CTR(%) = 20. That means for every $20 increase in CPM, CPC increases by exactly $1. Mathematically, this relationship is linear, which we can write as y = b × x, where CPC=y, CPM=x, and b = 1/(10 × CTR(%)). Expressed in small changes, Δy = bΔx. These symbols might look abstract, but the meaning is simple: the higher your CTR, the less each CPM fluctuation matters in absolute numbers.

Let’s make this more tangible. Suppose CPM increases by $5. If CTR = 2%, CPC goes up by $0.25. If CTR = 1%, CPC goes up by $0.50. If CTR = 0.5%, CPC jumps by a full dollar. The weaker the engagement, the more fragile the cost structure. This is why a low CTR campaign often feels unstable - because every movement in CPM gets magnified at the cost per click level.

The figure below shows these linear relationships. Each line represents a constant CTR. The steeper the line, the more exposed the system is to CPM turbulence.

Now, let’s see what if the constant is CPM, and we need to describe the relationship between CPC and CTR. Again, the equation is:

But now we assume that CPM isn’t a changeable parameter. Then, this equation has the form of an inverse proportional function:

Where k=CPM/10, y=CPC, x=CTR (%) . Here, we cannot expect to see equal changes in CPC when CTR changes for the same values. Let us draw this function for the k=1 value (when CPM=$10).

We see that CPC decreases while CTR increases. The first derivative of the function is -k/x2, the rate of CPC changing is rapid at first (for smaller x), and after some CTR value, it becomes pretty flat, so we can conclude that there is a CTR value when further increasing doesn’t produce a significant decrease in CPC.

But, we can make the view angle wider, and see if there is a space for improving CPC significantly, by the CTR increasing. If we look carefully at the chart, we’ll see that “the flattening” begins approximately at CTR=2%. On the other hand, improving CTR from, for example, 0.5% to 1% would decrease CPC from $2 to $1. Also, this curve changes for the different values of CPM. Let’s draw what happens when CPM is not $10, and we will use values of $20, $30, $50, $80, $100, $150.

Clearly, the curves become flattened earlier when CPM is relatively smaller. If you change, for example, CTR from 1% to 1.5% when CPM=$10, CPC will change from $1 to $0.67, but if CPM=$80, then CPC changes from $8 to $5.33 in the same CTR range!

The math above shows not only the proportional relationship between CPC and CPM/CTR, but also the absolute changes in CPC that occur as one of the other two metrics shifts - explaining when those changes are larger or smaller, and why. In real-world work, an experienced media buyer already develops an instinct for typical CPM ranges under certain campaign setups and learns to read the CTR/CPC combination that follows. This makes it easier to estimate how much CPC can realistically change under given conditions.

Of course, in practice, no metric ever stays perfectly constant. CPC variations always result from the joint movement of CPM and CTR. The winning formula is clear: lower CPM and higher CTR deliver the most clicks for the same spend. Yet “more clicks for the same money” isn’t always a victory. The quality of those clicks - ultimately measured by conversion rate - determines whether the achieved CPA truly meets the goal.

A campaign with the lowest CPC is often not the one delivering the best results. That’s why understanding the relationships between the metrics connecting impression and conversion helps you decide what to pause early and what deserves time and effort to fix. One thing is certain: optimization should never rely on a single metric.

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