CPM, CTR, CPC, and conversion rate are usually reported as separate line items on a dashboard. In reality, they’re links in a single chain — each one is mathematically derived from the ones before it. Understanding the chain makes it much easier to tell which number actually explains a change in cost or performance.

The chain, step by step

Starting from raw traffic and working toward cost:

  1. Impressions — how many times your ad was shown.
  2. CTR = Clicks ÷ Impressions — the share of impressions that turned into clicks.
  3. CPM = Spend ÷ Impressions × 1,000 — what you paid per 1,000 impressions, regardless of clicks.
  4. CPC = Spend ÷ Clicks — what you paid per click.
  5. Conversion Rate = Conversions ÷ Clicks — the share of clicks that turned into conversions.
  6. CPA = Spend ÷ Conversions — what you paid per conversion.

Because of how these are defined, CPC can also be written purely in terms of CPM and CTR:

CPC = CPM ÷ (1,000 × CTR)

And CPA can be written purely in terms of CPC and conversion rate:

CPA = CPC ÷ Conversion Rate

Chain them together and you get the whole funnel’s cost structure from just three independent inputs: CPM, CTR, and conversion rate.

A worked example

Suppose a campaign has:

  • Impressions: 500,000
  • CPM: $20 → Spend = 500,000 × $20 ÷ 1,000 = $10,000
  • CTR: 2% → Clicks = 500,000 × 0.02 = 10,000
  • Check: CPC = $10,000 ÷ 10,000 = $1.00, which matches CPM ÷ (1,000 × CTR) = $20 ÷ (1,000 × 0.02) = $1.00 ✓
  • Conversion Rate: 5% → Conversions = 10,000 × 0.05 = 500
  • CPA = $10,000 ÷ 500 = $20.00, which matches CPC ÷ Conversion Rate = $1.00 ÷ 0.05 = $20.00 ✓

Both cross-checks land on the same number, because they’re the same underlying arithmetic expressed two different ways — not a coincidence, an identity.

Why this matters for diagnosing changes

When CPA or CPC moves, the chain tells you exactly where to look:

  • A CPC change traces back to CPM (cost of exposure) and/or CTR (ad relevance/appeal).
  • A CPA change traces back to CPC (covered above) and/or conversion rate (what happens after the click).

Rather than treating “performance got worse” as one vague problem, the chain lets you ask a specific, answerable question: did this change because traffic got more expensive, because fewer people clicked, or because fewer clicks converted? Those point to different fixes.

Try it with your own numbers

The CPM, CTR, CPC, and Conversion Rate calculators each handle one link in this chain. To see the whole chain analyzed together across two periods — with the exact (not approximated) percentage breakdown — use the Marketing Performance Diagnostic.