Minimum detectable effect (MDE) calculator

Find the smallest effect your A/B test can detect with the users you have. Need a sample size instead? Calculate it →

Experiment setup

Baseline conversion rate

Control group's conversion rate (0%–100%)

Total sample size

The total number of users available, across both groups.

Proportion in test group

Control group: 50%

Test settings

α = 0.05
Power = 0.80
Two-sided

Minimum detectable effect

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Expected conversion rate, test

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Per group

Control: -⁠-⁠-⁠-
Test: -⁠-⁠-⁠-

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When to use it

Use this calculator when your outcome is binary — for example, converted or not, signed up or not, or active on day 7 — and your total sample size is fixed or limited rather than freely chosen.

This calculator is especially useful when:

Test duration is fixed, such as for a one-week campaign or seasonal promotion.
Traffic is limited, such as on a low-traffic page, within a niche segment, or for a B2B product.
You want to assess power before launching, to determine whether the test can detect a meaningful effect.
You need to set realistic expectations about which effects the test can and cannot detect.
You are deciding whether to increase traffic, extend the test, or test a bolder change.

If you already know the effect you want to detect and need to find the required sample size instead, use the sample size calculator.

Assumptions

The calculation assumes:

Random assignment: observations are independently assigned to the two groups.
Independent observations: each randomized unit contributes one observation, and observations from different units are assumed to be independent.
A sufficiently large sample: the calculation uses a normal approximation to the binomial. For very small expected counts, treat the result as approximate.

How the calculation works

The calculator uses the normal approximation for comparing two proportions. Given the sample size of each group, it finds the smallest increase in conversion rate that the test can detect with the specified power. Because the formula cannot be rearranged to solve for the test conversion rate directly, the calculator solves it numerically.

Detectable effect (solved numerically): Two-sided: n1 = [ z1−α/2·√[p̄(1−p̄)(1 + 1/r)] + z1−β·√[p1(1−p1) + p2(1−p2)/r] ]²(p2 − p1)²
One-sided: n1 = [ z1−α·√[p̄(1−p̄)(1 + 1/r)] + z1−β·√[p1(1−p1) + p2(1−p2)/r] ]²(p2 − p1)²
n₁ and n₂ are already fixed — from the total sample size you entered, split by the allocation ratio. This is the sample-size calculator's own equation, solved for p₂ instead of n₁. Because it cannot be rearranged to isolate p₂, the calculator narrows in on it numerically: it tries values of p₂ until both sides balance. A one-sided test assumes the effect is an increase over the baseline. A two-sided test also reports the detectable increase — because the formula's variance depends on p₂, the detectable decrease is a slightly different size, but a decrease of similar magnitude would also be detectable.
n₁ and n₂ are the control and test-group sizes: n₂ = round(N·w), n₁ = N − n₂, where N is the total sample size and w is the test-group share you enter.
r = n₂ / n₁ is the allocation ratio, computed from the test-group share: r = w/(1−w), where w = n₂/(n₁+n₂).
p₁ is the baseline conversion rate, and p₂ is the detectable conversion rate in the test group (solved for).
z1−α/2 and z1−α are the critical values for two-sided and one-sided tests, and z1−β is the standard normal value corresponding to the desired power (e.g. 0.84 for 80%).
Pooled proportion: p̄ = p1 + r·p21 + r
The proportion the equation's first term uses, under the null hypothesis that both groups convert at the same rate. At r = 1, p̄ is the simple average of p₁ and p₂; away from it, it is the weighted average shown here.
Lift and absolute difference: Lift = (p2 − p1)p1
Absolute difference = p2 − p1
The calculator reports the lift, and the test-group conversion rate it implies, p₂ = p₁ + absolute difference. The absolute difference is the same effect on the conversion rate's own scale, in percentage points. If the baseline conversion rate is 0%, lift has no baseline to be a share of — the calculator shows the detectable test-group rate instead.

Interpreting the output

The detectable lift is the smallest relative improvement your A/B test can reliably detect with the available sample size. The expected value in the test group — a conversion rate, a mean or a ratio — shows the same effect on the metric's own scale.

If the true effect is at least as large as the minimum detectable effect, your test has a probability of at least the selected statistical power (for example, 80%) to produce a statistically significant result. Smaller effects can still reach statistical significance, but with a lower probability.

Compare the detectable lift with the effect you realistically expect from the change. If the detectable lift is larger than the expected effect, the test is underpowered and is likely to miss a real improvement. In that case, consider increasing the sample size, running the test longer, or testing a bolder change.

Worked example

Suppose your baseline conversion rate is 10% and your test can reach a total of 7,682 users, split evenly.

Baseline conversion rate: 10%
Total sample size: 7,682
Significance level (α): 0.05
Power (1 − β): 0.80
Proportion in test group: 50% (equal allocation)

With 3,841 users per group, the smallest detectable lift is 20.00% — a conversion rate of 12.00%, an absolute difference of 2.00 percentage points.

If the true effect is at least a 20.00% lift, this sample size gives you an 80% probability of detecting it as statistically significant. A smaller true effect would still be worth having, but this test is not powered to reliably catch it.

When to use it

Use this calculator when your outcome is continuous — for example, revenue per user, session duration, or time on page — and your total sample size is fixed or limited rather than freely chosen.

This calculator is especially useful when:

Test duration is fixed, such as for a one-week campaign or seasonal promotion.
Traffic is limited, such as on a low-traffic page, within a niche segment, or for a B2B product.
You want to assess power before launching, to determine whether the test can detect a meaningful effect.
You need to set realistic expectations about which effects the test can and cannot detect.
You are deciding whether to increase traffic, extend the test, or test a bolder change.

If you already know the effect you want to detect and need to find the required sample size instead, use the sample size calculator.

Assumptions

The calculation assumes:

Random assignment: observations are independently assigned to the two groups.
Independent observations: each randomized unit contributes one observation, and observations from different units are assumed to be independent.
Approximately normal distribution: the calculation relies on the sampling distribution of the mean being approximately normal, which holds well for reasonably large samples even if the underlying metric is skewed.
One standard deviation for both groups: the form takes a single σ, so the design assumes the test group's spread matches the control's. If the change is likely to alter the spread, use the larger of the two values you expect.
Welch's degrees of freedom: the design plans for a Welch's t-test, the analysis that does not assume equal variances, exactly as the sample size calculator does. With one σ this changes only the degrees of freedom; on an even split they equal n₁ + n₂ − 2, and on an uneven one they are smaller, so the detectable effect is a little larger.

How the calculation works

The calculator uses the noncentral t-distribution. Given the sample size of each group, it finds the smallest effect for which the power reaches the target value. Unlike the binary KPI's search, this one always has a solution: power rises toward 1 as the effect size grows without bound, so the calculator never has to report that no detectable effect exists for a given sample size.

Noncentrality parameter (λ): λ = d√[n1n2(n1 + n2)]
Determines how far the expected effect is from the null hypothesis, based on the effect size and the two sample sizes — which are already fixed here, from the total you entered. A larger λ means the effect is easier to detect, so power increases.
Two-sided power: power = 1 − Ft(t1−α/2, df; df, λ)
The significance level is split between both tails, and power counts a significant result in the direction of the effect. The chance of one in the opposite direction is negligible at any useful power and is not counted — the same convention as R's power.t.test and as the sample size calculator.
One-sided power: power = 1 − Ft(t1−α, df; df, λ)
Calculates the probability of detecting an effect in the specified direction at the given significance level. The full significance level is placed in one tail, so a one-sided test can detect a smaller effect with the same sample size.
Absolute difference and lift: δ = d·σ
Lift = δμ0
d, the standardised effect size, is solved for numerically — the smallest value for which the power above reaches the target — then converted back to your metric's own units. A one-sided test assumes the effect is an increase over the baseline. A two-sided test also reports the detectable increase, but here the detectable decrease is exactly the same size — the noncentral-t power formula is symmetric in the sign of the effect, unlike the binary KPI's. If the baseline mean is not above 0, lift has no meaningful baseline to be a share of — the calculator shows the expected test-group mean instead.
Fₜ(·; df, λ) is the cumulative distribution function of the noncentral t-distribution.
tp, df is the p-th quantile of the central t-distribution.
df = (1/n₁ + 1/n₂)² / [ (1/n₁)²/(n₁−1) + (1/n₂)²/(n₂−1) ] is Welch's degrees of freedom with one standard deviation for both groups; it equals n₁ + n₂ − 2 on an even split.
d = δ / σ is the standardised effect size (Cohen's d), solved for.
δ is the detectable absolute difference in means, and μ₀ is the baseline mean.
σ is the standard deviation of the metric across individual users (or whatever your unit of randomisation is) — not the standard error, and not the standard deviation of daily aggregates.
n₁ and n₂ are the control and test-group sizes: n₂ = round(N·w), n₁ = N − n₂, where N is the total sample size and w is the test-group share you enter.

Interpreting the output

The detectable lift is the smallest relative improvement your A/B test can reliably detect with the available sample size. The expected value in the test group — a conversion rate, a mean or a ratio — shows the same effect on the metric's own scale.

If the true effect is at least as large as the minimum detectable effect, your test has a probability of at least the selected statistical power (for example, 80%) to produce a statistically significant result. Smaller effects can still reach statistical significance, but with a lower probability.

Compare the detectable lift with the effect you realistically expect from the change. If the detectable lift is larger than the expected effect, the test is underpowered and is likely to miss a real improvement. In that case, consider increasing the sample size, running the test longer, or testing a bolder change.

Worked example

Suppose your baseline mean is 10, with a standard deviation of 1, and your test can reach a total of 128 users, split evenly.

Baseline mean: 10
Standard deviation: 1
Total sample size: 128
Significance level (α): 0.05
Power (1 − β): 0.80
Proportion in test group: 50% (equal allocation)

With 64 users per group, the smallest detectable absolute difference is 0.50 — a 5.00% lift, for an expected test-group mean of 10.50.

If the true effect is at least a 5.00% lift, this sample size gives you an 80% probability of detecting it as statistically significant. A smaller true effect would still be worth having, but this test is not powered to reliably catch it.

When to use it

Use this calculator when your outcome is a ratio metric — a value calculated as one quantity divided by another, measured per randomization unit — for example, revenue per session, clicks per impression, or items purchased per session — and your total sample size is fixed or limited rather than freely chosen.

This calculator is especially useful when:

Test duration is fixed, such as for a one-week campaign or seasonal promotion.
Traffic is limited, such as on a low-traffic page, within a niche segment, or for a B2B product.
You want to assess power before launching, to determine whether the test can detect a meaningful effect.
You need to set realistic expectations about which effects the test can and cannot detect.
You are deciding whether to increase traffic, extend the test, or test a bolder change.

If you already know the effect you want to detect and need to find the required sample size instead, use the sample size calculator.

Assumptions

The calculation assumes:

Random assignment: observations are independently assigned to the two groups.
Independent observations: each randomization unit contributes its own numerator/denominator pair, and different units are assumed to be independent of each other.
Equal variance between groups: the same sd is assumed for both groups — the design assumes the treatment shifts the ratio without changing its variance.
Approximately normal distribution: the calculation relies on the delta-method approximation for the ratio's variance (a z approximation), which is well-behaved for reasonably large samples but slightly optimistic for very small ones.

How the calculation works

The calculator uses the same normal approximation as the ratio KPI's sample-size design, based on the baseline ratio and its standard deviation. Because that formula is already a closed-form expression for the sample size, finding the detectable effect is the same equation solved for the effect instead.

Detectable effect: Two-sided: Δ = (z1−α/2 + z1−β)·sd·√[1/n1 + 1/n2]
One-sided: Δ = (z1−α + z1−β)·sd·√[1/n1 + 1/n2]
n₁ and n₂ are already fixed — from the total sample size you entered, split by the allocation ratio. This is the sample-size calculator's own equation, solved for Δ instead of n₁, at the two group sizes the total actually splits into — so when the total does not divide evenly, the result is the effect those whole groups can detect rather than the one an exact split would. A one-sided test assumes the effect is an increase over the baseline; a two-sided test reports the detectable increase, and here the detectable decrease is exactly the same size — the formula is symmetric in the sign of the effect.
n₁ and n₂ are the control and test-group sizes: n₂ = round(N·w), n₁ = N − n₂, where N is the total sample size and w is the test-group share you enter.
The ratio's standard deviation (sd): sd² = (σX² − 2R·Cov(X, Y) + R²σY²)μY²
R = μXμY
This is the input most likely to get entered wrong: sd is the ratio's own per-user standard deviation, not the standard error of the ratio and not a standard deviation computed per session or per order. The ratio's denominator (sessions, orders, …) is not the unit of randomisation — users are — so a naive standard deviation of the per-session or per-order ratio understates the true variance. The delta method derives the ratio's actual per-user variance from the numerator's and denominator's own variances and how they covary. The helper calculator on this page computes sd for you, from either raw per-user data or these same summary statistics.
X is each user's numerator total (e.g., revenue) and Y is each user's denominator total (e.g., sessions); the ratio metric is X/Y, and R = μXμY is the baseline ratio.
σX² and σY² are the variances of X and Y across users, and Cov(X, Y) is their covariance — how much a user with an above-average numerator also tends to have an above-average denominator.
Lift and expected ratio: Lift = ΔR1
R2 = R1 + Δ
The detectable effect, reported as a proportion of the baseline ratio and as the smallest test-group ratio the design can detect. For a two-sided test, the same-size decrease is also detectable — the design's detectable range is R₁ ± Δ. If the baseline ratio is not above 0, lift has no meaningful baseline to be a share of — the calculator shows the expected test-group ratio instead.
R₁ is the baseline (control) ratio, and R₂ is the smallest test-group ratio the design can detect.

Interpreting the output

The detectable lift is the smallest relative improvement your A/B test can reliably detect with the available sample size. The expected value in the test group — a conversion rate, a mean or a ratio — shows the same effect on the metric's own scale.

If the true effect is at least as large as the minimum detectable effect, your test has a probability of at least the selected statistical power (for example, 80%) to produce a statistically significant result. Smaller effects can still reach statistical significance, but with a lower probability.

Compare the detectable lift with the effect you realistically expect from the change. If the detectable lift is larger than the expected effect, the test is underpowered and is likely to miss a real improvement. In that case, consider increasing the sample size, running the test longer, or testing a bolder change.

Worked example

Suppose your baseline revenue-per-session ratio is $25, with a delta-method standard deviation of 42 per user, and your test can reach a total of 8,862 users, split evenly.

Baseline ratio: $25
Standard deviation: 42
Total sample size: 8,862
Significance level (α): 0.05
Power (1 − β): 0.80
Proportion in test group: 50% (equal allocation)

With 4,431 users per group, the smallest detectable lift is 10.00% — an absolute difference of $2.50, for an expected test-group ratio of $27.50. This is the sample size calculator's ratio example run in reverse: there, a 10% lift at this baseline and standard deviation needs 4,431 users per group.

If the true effect is at least a 10.00% lift, this sample size gives you an 80% probability of detecting it as statistically significant. A smaller true effect would still be worth having, but this test is not powered to reliably catch it.

Frequently asked questions

What is a minimum detectable effect?

The smallest true effect a test is powered to catch. Below it, a real effect is more likely than not to produce a result that fails to reach significance — not because nothing happened, but because the sample was too small to tell the difference from noise reliably.

How is this different from the sample size calculator?

Same statistics, opposite direction. The sample size calculator takes the effect you want to detect and tells you how many users you need. This calculator takes the number of users you already have and tells you the smallest effect that sample size can detect. Use whichever one matches which number is fixed for you.

What if the detectable lift is larger than I expect the real effect to be?

The test is underpowered for that effect: it is more likely than not to come back inconclusive even if the change genuinely works. The options are the same three that always apply — extend the test to collect more sample, increase the traffic entering it, or test a larger change that would produce a bigger effect.

Can I use this for a test that is already running?

Yes, to set expectations for how it will land — enter the total sample size you expect by the end of the test, not the count so far. It is not a substitute for checking results early: reading significance before the test reaches its planned sample, and stopping as soon as it looks significant, inflates the false-positive rate regardless of what this calculator says the design can detect.

Related calculators

A/B test sample size
Size an experiment before you launch, for a binary, continuous or ratio KPI — each with its own design and its own assumptions.
A/B test analysis
Read a finished experiment for a binary, continuous or ratio KPI — the lift, its confidence interval and a p-value.
SRM check
Check whether your experiment actually split traffic the way you configured it — the first thing to run, before any metric.

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The Bell Experiments MCP server gives your assistant the Bell Statistics engine: ask it to pick test and control markets, estimate the budget or read the lift in plain language, and get the answer with the assumptions behind it. A/B testing is next.

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We size, run and read experiments where the metric, the sample size and the decision rule are agreed before anyone looks at the data. A/B Testing

References

Fleiss, J. L., Levin, B., & Paik, M. C. (2003). Statistical Methods for Rates and Proportions (3rd ed.). Wiley.
Deng, A., Knoblich, U., & Lu, J. (2018). Applying the Delta Method in Metric Analytics: A Practical Guide with Novel Ideas. KDD '18, 233-242.

Minimum detectable effect (MDE) calculator

When to use it

Assumptions

How the calculation works

Interpreting the output

Worked example

When to use it

Assumptions

How the calculation works

Interpreting the output

Worked example

When to use it

Assumptions

How the calculation works

Interpreting the output

Worked example

Frequently asked questions

Related calculators

A/B test sample size

A/B test analysis

SRM check

Further reading

Four Ways to Improve Statistical Power in A/B Testing (without increasing test duration, duh)

Statistically speaking: How to (properly) report A/B testing results

Design geo tests without leaving Claude

Talk to the people who build these for a living

References

Minimum detectable effect (MDE) calculator

Calculator

When to use it

Assumptions

How the calculation works

Interpreting the output

Worked example

When to use it

Assumptions

How the calculation works

Interpreting the output

Worked example

When to use it

Assumptions

How the calculation works

Interpreting the output

Worked example

Frequently asked questions

Related calculators

A/B test sample size

A/B test analysis

SRM check

Further reading

Four Ways to Improve Statistical Power in A/B Testing (without increasing test duration, duh)

Statistically speaking: How to (properly) report A/B testing results

Design geo tests without leaving Claude

Talk to the people who build these for a living

References