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Marketing & Advertising CALCULATOR

A/B Test Sample Size Calculator

The sample is per variant for an equal-allocation two-sided normal approximation.

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Quick answer

The sample is per variant for an equal-allocation two-sided normal approximation.

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RESULT
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13,918 visitors per variant is the example result. The sample is per variant for an equal-allocation two-sided normal approximation. Baseline probability and relative uplift are different inputs; this is not a sequential-testing stopping rule.

Per-variant sample n = [zα × √(2 × p̄ × (1−p̄)) + zβ × √(p₁ × (1−p₁) + p₂ × (1−p₂))]² ÷ (p₂−p₁)², rounded up. p₂ = p₁ × (1 + relative uplift), p̄ = (p₁+p₂) ÷ 2. Two-sided normal approximation with equal allocation.
Purpose

The sample is per variant for an equal-allocation two-sided normal approximation.

Separating campaign efficiency from business profit

The sample is per variant for an equal-allocation two-sided normal approximation. Baseline probability and relative uplift are different inputs; this is not a sequential-testing stopping rule. Campaign ratios depend on the event being counted. A click, a submitted form, a qualified opportunity and a paying customer are separate outcomes. Combine spend and events from the same campaign window before comparing acquisition costs.

What the model includes

Per-variant sample n = [zα × √(2 × p̄ × (1−p̄)) + zβ × √(p₁ × (1−p₁) + p₂ × (1−p₂))]² ÷ (p₂−p₁)², rounded up. p₂ = p₁ × (1 + relative uplift), p̄ = (p₁+p₂) ÷ 2. Two-sided normal approximation with equal allocation. Attribution can credit revenue to several channels. Use one attribution definition for the comparison and keep refunds or cancelled orders consistent. An efficient advertising ratio can coexist with weak contribution after fulfilment. Read the result beside lead quality and the sales outcome. A lower cost is useful only when the counted event still represents the objective the campaign was built to achieve.

Example with the supplied inputs

Baseline conversion (%): 3; Minimum detectable uplift (%): 20; Confidence (%): 95; Statistical power (%): 80. Result: 13,918 visitors per variant. The values are illustrative.

Compare one changed input

Baseline conversion (%) changes from 3 to 3.3. The result becomes 12,610 visitors per variant. All other inputs remain fixed.

Calculation rule

Formula

Per-variant sample n = [zα × √(2 × p̄ × (1−p̄)) + zβ × √(p₁ × (1−p₁) + p₂ × (1−p₂))]² ÷ (p₂−p₁)², rounded up. p₂ = p₁ × (1 + relative uplift), p̄ = (p₁+p₂) ÷ 2. Two-sided normal approximation with equal allocation.

Inputs and output

Example inputs and entry conventions
Input Example value Entry convention
Baseline conversion (%) 3 Enter baseline conversion (%) on the percentage scale used in the formula (20 means 20%, not 0.20). Keep its base and reporting period consistent with the other inputs.
Minimum detectable uplift (%) 20 Enter minimum detectable uplift (%) on the percentage scale used in the formula (20 means 20%, not 0.20). Keep its base and reporting period consistent with the other inputs.
Confidence (%) 95 Enter confidence (%) on the percentage scale used in the formula (20 means 20%, not 0.20). Keep its base and reporting period consistent with the other inputs.
Statistical power (%) 80 Enter statistical power (%) on the percentage scale used in the formula (20 means 20%, not 0.20). Keep its base and reporting period consistent with the other inputs.

Output: 13,918 visitors per variant is the example result. The sample is per variant for an equal-allocation two-sided normal approximation. Baseline probability and relative uplift are different inputs; this is not a sequential-testing stopping rule. Unit: visitors per variant.

How to use the page

STEP 01

Collect the inputs

Gather Baseline conversion (%), Minimum detectable uplift (%), Confidence (%). Use one period and the units shown in the form.

STEP 02

Run the calculation

Enter the values and select the action. The calculation rule above explains how the inputs produce the result.

STEP 03

Compare a scenario

Change Baseline conversion (%) on its own, keeping the other inputs fixed. Read both results before changing another assumption.

Worked example

With the example inputs listed above, the result is 13,918 visitors per variant.

Change Baseline conversion (%) from 3 to 3.3 while keeping every other value fixed. The result becomes 12,610 visitors per variant. This comparison isolates that input; it does not forecast how other variables will respond.

Check the stated formula, units and limits before using the result in a decision.

Calculation and source notes

Keep the displayed formula, input units and model scope with the result. Corrections or questions can be sent through the request section on this page.

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CONTENT AND CORRECTIONS

Martzine Editorial Team

Martzine’s editorial work is led by Bilal Ahmad, founder of Martzine, with support from his team across content, research and technical development. Team members contribute according to the subject and assigned work, from practical explanations and source research to tool functionality and website improvements.

Martzine publishes and maintains the tools, calculators, references, resources and articles on this website. Our editorial work covers clear instructions, calculation assumptions, useful sources and corrections when an issue is identified.

A result depends on the inputs and the limits described on its page. If you notice a calculation error, broken feature, unclear explanation or information that needs correction, please send us the page link, the details and any supporting reference. We will assess the report and correct confirmed issues as soon as practical.

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