The Sainsbury Method in Media Planning: How to Calculate Unduplicated Net Reach

Imagine you’re running ad campaigns across Meta and Google Ads. Your Meta dashboard reports that your campaign reached 40% of your target market. Your Google Ads campaign reports that it reached 30% of the same market. When you report this to your CEO or client, what was your total campaign reach?

If your instinctive answer is “40% + 30% = 70%”, you have fallen into the most expensive trap in media planning: the double-counting illusion.

People do not live in separate internet boxes. The prospective buyer searching for your software on Google at 10:00 AM is the exact same person scrolling Instagram on their couch at 8:00 PM. If you simply add their reach numbers together, you count that person twice—inflating your reported audience and hiding your true customer acquisition costs.

To solve this, professional media planners use a classic mathematical framework: The Sainsbury Method (also known as the Random Duplication Formula). Here is how it works, why it matters, how to calculate it using simple 5th/6th-grade math, and how it compares to Max Reach.

1. The Core Principle: Flipping the Math

Trying to calculate how many people saw your ads across multiple channels by adding them up requires complicated Venn diagrams with overlapping slices. The math becomes a nightmare once you add a third or fourth channel like YouTube, LinkedIn, or programmatic display.

The genius of Trevor Sainsburyu2019s formula is that it completely flips the problem upside down:

Instead of calculating who SAW your ads, calculate the probability of who MISSED them on every single platform.

Think of it like this:

• If Platform A reaches 40% of your audience, that means 60% of people never saw it (0.60 unreached).
• If Platform B reaches 30% of your audience, that means 70% of people never saw it (0.70 unreached).

Now, what are the odds that a person in your target market completely missed your ads on both platforms? Assuming audience consumption overlaps randomly, you simply multiply the two unreached probabilities together:

Unreached Audience = 0.60 × 0.70 = 0.42 (42%)

If 42% of your total audience completely missed both campaigns, then everyone else must have seen your ad at least once:

Net Unduplicated Reach = 100% - 42% = 58%

Your true reach was not 70%u2014it was 58%. That 12% difference represents the shared audience who saw your ads on both Meta and Google.

2. The 5th/6th Grade Mental Model: The Paint Splash Room

If probability equations make your head spin, here is the absolute easiest way to understand the Sainsbury Methodu2014explained using standard 5th/6th-grade math that anyone can do on a phone calculator or napkin in 30 seconds.

Imagine a room with 100 people all wearing clean white T-shirts.

1. Channel 1 (Meta Ads) enters the room: They have a bucket of blue paint and splash it randomly across 40% of the room. 40 people now have blue paint on their shirts. That means 60 people still have spotless, clean white shirts.
2. Channel 2 (Google Ads) enters the room: They have a bucket of yellow paint and splash it across 30% of the room. But Google does not know who is already wearing blue. They splash paint randomly across the entire room.
3. The Math Question: Out of the 60 people who still had completely clean white shirts, how many did Google splash with yellow paint?
   

   30% of 60 people = 0.30 × 60 = 18 people

4. How many people survived untouched?
   

   60 clean people - 18 splashed people = 42 completely clean people left

5. So how many people in the room got paint on their shirt?
   

   100 total people - 42 clean people = 58 people reached!

That is the entire Sainsbury Method. No advanced calculus, no confusing Greek symbols. You simply calculate how many people kept their shirts clean, and subtract that from 100.

The Standard 6-Step Napkin Calculator (Do This in 30 Seconds)

Whenever a client, boss, or media planner asks you for the combined reach of multiple ad platforms, follow these exact 6 steps on your smartphone calculator:

3. The Master Sainsbury Formula

You can extend this formula across two, three, five, or ten different media vehicles. The universal mathematical formula is written as:

Where:

• 1 represents 100% of your total target market (the total audience “universe”).
• R₁, R₂, R₃… represent the individual reach percentage of each channel expressed as a decimal (e.g., 25% = 0.25).
• (1 – R) represents the percentage of people who were not reached by that specific channel.

4. Step-by-Step Example: A 3-Channel Digital Campaign

Let’s run through a realistic performance marketing scenario with real numbers.

Suppose you are an e-commerce brand or B2B company targeting a total defined audience of 2,000,000 professionals in the United States. You launch a coordinated 30-day paid media push across three channels:

• Channel 1 (Meta Ads): Reaches 45% of the market (R₁ = 0.45)
• Channel 2 (Google Search & PMax): Reaches 35% of the market (R₂ = 0.35)
• Channel 3 (YouTube Video Ads): Reaches 25% of the market (R₃ = 0.25)

If you naively added those numbers together: 45% + 35% + 25% = 105%. You cannot reach 105% of a population. Let’s calculate the real net reach using Sainsbury’s formula:

Step 1: Calculate the “Unreached” Percentage for Each Channel

• Meta Unreached: 1 - 0.45 = 0.55 (55% missed it)
• Google Unreached: 1 - 0.35 = 0.65 (65% missed it)
• YouTube Unreached: 1 - 0.25 = 0.75 (75% missed it)

Step 2: Multiply the Unreached Shares Together

Combined Non-Reach = 0.55 × 0.65 × 0.75 = 0.2681 (26.81%)

Only 26.81% of your 2,000,000 target market completely avoided seeing your brand across all three platforms.

Step 3: Subtract from 1 to Get Net Unduplicated Reach

Net Reach (%) = 1 - 0.2681 = 0.7319 = 73.19%

Step 4: Convert Percentage to Total Unique People

Now multiply your net reach percentage by your total audience universe size:

Total Unique People Reached = 73.19% × 2,000,000 = 1,463,800 Unique Humans

5. Sainsbury Net Reach vs. Max Reach: What’s the Difference?

In high-stakes media planning and boardroom pitch decks, you will frequently hear agency leads cite “Max Reach” alongside or instead of “Net Reach”. Confusing these two numbers will derail your budget forecasts and lead to wildly unrealistic sales expectations.

What Is Max Reach? (Theoretical Maximum Reach)

Max Reach (also known as Gross Reach or Zero-Duplication Reach) represents the absolute highest number of unique people your campaign could possibly reach if and only if there was ZERO audience overlap between your platforms.

Under the Max Reach assumption, every single person who saw your ad on Meta never uses Google, and every person who searched on Google never opens Instagram. It assumes the two audiences are completely mutually exclusive.

How to Calculate Max Reach:

Max Reach (%) = R1 + R2 + R3 + ... + Rn (Capped at 100% of the Market Universe)
Max Reach (People) = Reach(Platform A) + Reach(Platform B) + Reach(Platform C)

If Platform A reaches 400,000 people and Platform B reaches 300,000 people out of a 1,000,000 audience universe:

Max Reach = 400,000 + 300,000 = 700,000 people (70% Max Reach)

The Three Reach Tiers: Min Reach, Sainsbury Reach, and Max Reach

Every multi-channel ad campaign exists within a mathematical boundary between a theoretical minimum and a theoretical maximum:

Why Media Buyers Must Compare Sainsbury Reach to Max Reach

The gap between your Max Reach and your Sainsbury Net Reach reveals your Audience Duplication Rate:

Duplication Rate = (Max Reach - Sainsbury Net Reach) / Max Reach
In our example: (70% - 58%) / 70% = 12% / 70% = 17.1% Overlap

How you interpret this overlap depends entirely on your campaign objective:

• For Brand Awareness & Market Penetration: A high duplication rate indicates media inefficiency. If your goal is planting your brand in front of as many new eyes as possible, high overlap means you are paying multiple platforms to talk to the same people when you should be expanding into new channels or creative angles.
• For B2B & High-Ticket Conversion: High duplication is your greatest asset. High-ticket B2B buyers rarely convert on first touch. Overlap means your prospect searches on Google, sees your client case study on LinkedIn, and watches your founder testimonial on Instagram. That duplication drives effective multi-touch frequency that builds trust and closes pipeline.

6. How to Calculate Average Ad Frequency

Once you know your true unduplicated reach, you can immediately calculate one of the most critical metrics in media buying: Average Exposure Frequency.

Frequency tells you how many times the average person saw your message across your entire media mix:

Average Frequency = Total Gross Impressions / Total Unduplicated Reach

For example, if your three campaigns generated a combined 5,855,200 total impressions, and you reached 1,463,800 unique people:

Average Frequency = 5,855,200 / 1,463,800 = 4.0 Impressions Per Person

Knowing that your audience saw your ad 4 times on average gives you confidence that your message penetrated their awareness without causing severe creative fatigue (which typically occurs at frequency 7+).

7. What Are the Limitations of the Sainsbury Method?

While the Sainsbury method is an essential back-of-the-envelope tool for media planning and financial forecasting, you must keep one key assumption in mind:

• The Random Duplication Assumption: The formula assumes that audience overlap occurs completely by random chance. In real life, media consumption is often correlated. For instance, tech workers who use LinkedIn heavily are also much more likely to use YouTube than the average population, meaning real-world overlap might be slightly higher than pure probability predicts.
• When to Use It: Use the Sainsbury Method when budgeting multi-channel digital campaigns, evaluating cross-platform pitch proposals, or when you do not have access to multi-million dollar unified identity graphs.

Frequently Asked Questions

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“text”: “Max Reach is the simple sum of all individual channel reaches assuming zero audience overlap (the theoretical ceiling). Net Reach, calculated using the Sainsbury Method, subtracts the overlapping audience who saw ads across multiple channels to report the true unique individuals exposed.”
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“text”: “Walled gardens report accurate logged-in reach only within their own ecosystem. When combining Meta Ads with Google Ads, YouTube, and LinkedIn, platforms do not share cross-network identity data. The Sainsbury Method remains the fastest mathematical model to estimate cross-network deduplicated reach.”
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