How to calculate CPM: formula, worked examples and reverse maths

The formula

CPM = (total cost ÷ impressions) × 1,000.

The M stands for mille, Latin for a thousand, so CPM is literally cost per thousand impressions. You will also see it written as cost per thousand, or described in plain words as the price of a thousand contacts. It is all the same metric. Display inventory is priced per thousand because the price of a single impression is a fraction of a cent.

An example: $450 spent for 180,000 impressions. 450 ÷ 180,000 is $0.0025 per impression, and multiplied by 1,000 that is a CPM of $2.50.

Most real questions run the other way round, and the formula rearranges into two more:

You know	You want	Formula
Cost and impressions	CPM	cost ÷ impressions × 1,000
Budget and CPM	Impressions	budget ÷ CPM × 1,000
Impressions and CPM	Cost	impressions ÷ 1,000 × CPM

A $2,000 budget at an $8 CPM buys 2,000 ÷ 8 × 1,000 = 250,000 impressions. Booking 400,000 impressions at $5.50 costs 400,000 ÷ 1,000 × 5.50 = $2,200.

From budget to cost per acquisition

CPM on its own prices attention. The useful exercise is to follow it through to what you actually pay for a customer. Here is one plan, step by step: a $3,000 budget, a $9 CPM, a 0.9% click-through rate and a landing page that converts 3% of visitors.

1. Impressions: 3,000 ÷ 9 × 1,000 = 333,333.
2. Clicks: 333,333 × 0.009 = 3,000.
3. Cost per click: 3,000 ÷ 3,000 = $1.00.
4. Conversions: 3,000 × 0.03 = 90.
5. Cost per acquisition: 3,000 ÷ 90 = $33.33.

Now change one input at a time and watch the last line.

Scenario	Clicks	Conversions	CPA
Plan as above	3,000	90	$33.33
CPM rises a third, to $12	2,250	67.5	$44.44
CTR falls a third, to 0.6%	2,000	60	$50.00
CTR rises a third, to 1.2%	4,000	120	$25.00

A third more expensive inventory raises CPA by a third. A third fewer clicks from the same impressions raises it by half. CPA is CPM divided by (CTR × conversion rate), so a given percentage fall in CTR or conversion rate hurts more than the same percentage rise in CPM. In practice that means the creative and the landing page, which you control, usually swing the outcome more than the CPM the auction sets.

CPM, CPC and CTR

The three are linked by one relationship: CPC = CPM ÷ (1,000 × CTR), with CTR as a decimal. At a $6 CPM, a 0.5% CTR gives a cost per click of 6 ÷ 5 = $1.20, and a 1.5% CTR gives 6 ÷ 15 = $0.40. The inventory did not get cheaper; the ad simply earned three times the clicks from it.

If you buy by the click instead, you can express the price as an effective CPM: eCPM = CPC × CTR × 1,000. A $0.60 CPC at a 1.2% CTR is 0.60 × 0.012 × 1,000 = $7.20 eCPM. That is the number to put next to a quoted CPM when comparing a click-priced buy with an impression-priced one.

Publishers work from the other side. Their figure is usually RPM, earnings per thousand pageviews or sessions depending on the report. It is not the CPM an advertiser pays: it blends the price of the ads with how many load on a page and how often they fill.

Reach, frequency and what an impression is

An impression is a view, not a person. Impressions equal reach multiplied by average frequency. The 250,000 impressions bought in the first example, at an average frequency of 2.5, reached 100,000 people.

Price that by people and it looks different: $2,000 ÷ 100,000 × 1,000 = $20 per thousand people reached, two and a half times the headline $8 CPM. Neither number is wrong, but only one is the cost of reaching a thousand different people.

Billed impressions are not viewed impressions

A served impression counts and is billed even if it never enters the viewport. vCPM puts the denominator right: cost ÷ viewable impressions × 1,000. If that $450 bought 180,000 served impressions and 60% were viewable, the viewable count is 108,000 and the vCPM is $4.17, not the $2.50 on the invoice.

Viewability definitions differ by platform and format. A common industry standard for display counts an ad as viewable once at least half of its pixels are on screen for one continuous second.

Mistakes that skew the number

• Forgetting the × 1,000. The result is a “CPM” of $0.0025, and the plan built on it is off by three orders of magnitude.
• Comparing across formats. Video, display, native and feed placements have structurally different CPMs, as do audiences and countries. Compare like with like.
• Judging a performance goal by CPM. A low CPM is cheap attention, and worth having only if the attention converts.
• Treating budget ÷ CPM as guaranteed. It is a forecast. Delivery depends on the auction, targeting breadth and pacing.

The CPM calculator solves any of the three directions and adds CPC and CTR when you give it clicks. To tag the campaign so the results arrive sorted, build the links with the UTM builder; to check whether the resulting CPA is affordable, see the ROAS calculator and the CAC calculator.