Minimum Detectable Effect Calculator
The formula
What the minimum detectable effect tells you
The flip of the sample-size question: with this traffic and power, what is the smallest lift the test can honestly prove?
Calculation: MDE = (z_conf + z_power) × √(2p(1−p)/n). Enter your inputs and every substitution is shown below the result.
Reading the result
If the MDE is a 20% relative lift, small steady improvements are undetectable by design — either pool metrics, extend the test, or stop testing the tweak.
Rules of thumb: Well-run programs target MDE 5–15% relative on primary metrics
Limitations and best practice
Teams read a non-significant result as “no effect” when it means “no effect this size” — the MDE is the sentence’s missing ending.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
Should I power on revenue or conversion?
Do variance-reduction tricks shrink the MDE?
Source & methodology
Experimental-design arithmetic (MDE form).
Minimum Detectable Effect: what this tool answers
You are here because you need a specific number, and you want to see how it was produced before you rely on it. There are plenty of pages about Minimum Detectable Effect; almost none of them show the working. This one does: the formula, every input, a fully computed example, and a sensitivity analysis calculated live from this engine’s own defaults.
A calculation like this one is worth roughly as much as a careful sentence: it forces several vague considerations into one comparable quantity. Once Minimum Detectable Effect is on the table, the argument can stop being about impressions.
Most confusion about Minimum Detectable Effect comes from mixing up the input you control with the input you merely observe. The formula treats them identically, but your decisions should not: one deserves measurement, the other deserves a defensible estimate.
What makes a calculation page trustworthy is that its copy is derived from its own arithmetic: here minimum detectable effect = 0.79 pts, recomputed every time a field changes, and the sensitivity section ranks the inputs that move the result — Confidence level first, at ≈27.2 % of the headline for a ten-percent error either way in that input. Read the sections in order and you will be able to reproduce every figure by hand.
Every input in Minimum Detectable Effect, and what it does to the answer
The engine implements a single stated model: MDE = (z_conf + z_power) × √(2p(1−p)/n). There is no hidden coefficient and no login-gated precision — the formula printed is the formula executed, which is also what makes the result citable.
Baseline rate (%) (example value 4) is a measured number in the unit named by the label; the formula does not convert for you. Enter it exactly as your document states it — quoted annual, monthly and effective rates are three different numbers.
Visitors per arm (example value 14,437) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. The example value is there to demonstrate the mechanics, not to describe your situation — overwrite it.
Statistical power (%) (example value 85) is a measured number in the unit named by the label; the formula does not convert for you. Rates are the most mis-transcribed input on any page like this; copy it from the document rather than retyping from memory.
Confidence level (%) (example value 100) is a quantity rather than a category — precision here is cheap and worth having. Rates are the most mis-transcribed input on any page like this; copy it from the document rather than retyping from memory.
The default Minimum Detectable Effect calculation, written out in full
The tool prints its own working; this is the same arithmetic on the example values, reproduced so you can follow it by hand. Starting figures: Baseline rate (%), Visitors per arm, Statistical power (%), Confidence level (%). The computed minimum detectable effect comes out at 0.79 pts, which the interpretation band labels “Your test proves lifts ≥ 0.79 pts (19.7% relative) — anything smaller passes invisibly”.
- MDE = (2.58 + 0.84) × √(2×0.0400×0.9600 ÷ 14437)
- = 0.79 pts absolute
As relative lift over baseline — 19.7 %. Compare it against the main result of 0.79 pts before drawing conclusions.
n per arm to halve the MDE — 57,748.0. This is the number experienced users quote when the headline alone would mislead.
MDE at 99% confidence instead — 0.79 pts. If your inputs change, this is usually the first companion figure to move.
Overwrite any input above and every line of this example updates with it — the substitution is live, not a screenshot of somebody else’s numbers.
The Minimum Detectable Effect corridor: your result across a realistic band
Read this table as the practical error bar on the headline figure. It answers the question people actually have after seeing a single number: how wrong could this be if the main input is off by ten or twenty percent?
| Confidence level setting | Minimum detectable effect |
|---|---|
| 80 % of the example value | 0.57 pts |
| 90 % of the example value | 0.57 pts |
| example inputs | 0.79 pts |
| 110 % of the example value | 0.79 pts |
| 120 % of the example value | 0.79 pts |
That spread — 0.57 pts at the low end, 0.79 pts at the high — is what a careful read of Minimum Detectable Effect looks like: a band you can state out loud, with the reason for each edge. Reproduce it in the form above by editing Confidence level alone; the substitution steps will follow your figures exactly.
The levers behind Minimum Detectable Effect, ranked by effect
Generic advice says “it depends on your inputs”; this section says exactly how much. Each field was perturbed by ±10 % in isolation and the minimum detectable effect recomputed, so the ranking below is measured rather than asserted. It is the fastest honest answer to “what matters most in Minimum Detectable Effect?” — and it is specific to these defaults, because sensitivity moves with the starting point.
- Confidence level +10 % → Minimum Detectable Effect = 0.79 pts · −10 % → 0.57 pts (the minimum detectable effect shifts ≈27.2 %)
- Nudge Statistical power by ±10 % and Minimum Detectable Effect lands between 0.71 pts and 0.89 pts (sensitivity ≈12.9 %)
- Visitors per arm: ten percent up gives 0.75 pts, ten percent down gives 0.83 pts — ≈5.4 % of the minimum detectable effect either way
- Baseline rate: ten percent up gives 0.83 pts, ten percent down gives 0.75 pts — ≈4.9 % of the minimum detectable effect either way
Confidence level is the dominant lever here: ten percent either way moves the result by about 27.2 %, from 0.57 pts to 0.79 pts. Spend your verification effort there first, and treat Statistical power as the second priority (≈12.9 % per ten percent). Everything below that can stay approximate, which is a licence to stop chasing data that would not change the decision.
Is your Minimum Detectable Effect good — reading the result bands
Nobody acts on a bare figure — they act on a figure with a comparison attached. The verdict attached to the default calculation — “Your test proves lifts ≥ 0.79 pts (19.7% relative) — anything smaller passes invisibly” — is one band on a ladder your own figure may sit somewhere else on. How much of that band is luck? On Confidence level alone ten percent either way covers 0.57 pts to 0.79 pts. The practical reading rules: compare against your own history before comparing against other people; treat band boundaries as zones, not walls — one point on the wrong side of a threshold rarely changes a real outcome; and when a companion output contradicts the headline, believe the pair.
In Business & Entrepreneurship, Minimum Detectable Effect is one instrument in an orchestra: on its own it is a number, next to As relative lift over baseline and n per arm to halve the MDE it becomes a diagnosis. The tools linked above exist so the headline never has to carry that weight alone.
Common mistakes with Minimum Detectable Effect (and the fix)
Teams read a non-significant result as “no effect” when it means “no effect this size” — the MDE is the sentence’s missing ending. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Comparing a Minimum Detectable Effect computed here with a figure from another source that uses different conventions. Same name, different denominator — the disagreement is usually in the definitions, not the data.
This model has its own particular trap: Confidence level carries ≈27.2 % of the response per ten percent of error, so effort spent elsewhere is largely decorative.
Another is comparing across contexts: a Minimum Detectable Effect computed with one set of conventions should never be lined up against a figure computed with another. Check the inputs behind both before ranking them.
A quick check for any Minimum Detectable Effect figure
- State, in one sentence, which convention each rate, unit or period in the form is using.
- Compare the result with one independent method or published benchmark.
- Check Confidence level before anything else: it is the measured dominant input, ≈27.2 % of Minimum Detectable Effect per ten percent.
- Compare the output against one published benchmark or a colleague’s independent estimate.
- Record the date and the inputs alongside the number so future-you knows what was assumed.
- Confirm the answer against one independent method or published benchmark for Minimum Detectable Effect.
Step by step: getting a trustworthy Minimum Detectable Effect out of this tool
Using a calculator well sounds trivial, but the difference between a decision-grade figure and a throwaway one lives entirely in the routine. The routine for Minimum Detectable Effect takes a minute to learn and applies to every input above.
Step 1 — start from evidence. The inputs behind Minimum Detectable Effect are baseline rate (%), visitors per arm, statistical power (%), confidence level (%). Write them down with their source next to each one; if you cannot name where a figure came from, that is the input most likely to be wrong. A result worth acting on survives having its two shakiest inputs halved.
Step 2 — compute the version you would not be embarrassed by. If a stranger audited your inputs, which set would you hand over? Enter that set, read the result, and treat everything else as upside. Write the assumptions in the same file as the result, and future arguments take minutes instead of meetings.
Step 3 — play with the inputs on purpose. Ten percent up, ten percent down, one field at a time. Within a few minutes you will know this calculation better than most people who quote its results. A figure with a date beside it becomes evidence; without one it stays an anecdote.
Step 4 — ask what would have to be true. Take the result you want and work backwards through the inputs until you find the assumption that produces it; then decide honestly whether that assumption is defensible. A figure nobody can reproduce is a figure nobody will act on twice.
Step 5 — record the context, not just the number. Note today’s date and the inputs alongside the 0.79 pts output. Six months from now the context is what turns this figure into a trend. Numbers are cheap to produce and expensive to retract; the extra minute is the cheapest insurance available.
From calculation to decision: where Minimum Detectable Effect earns its keep
In Marketing & Growth the figure computed here is usually the first one somebody asks to see. Having it — with the formula behind it — changes your position in the conversation from participant to reference. The input you reach for first is usually the one you measured longest ago.
Used properly this is a five-minute filter that saves weeks. Compute Minimum Detectable Effect, reject what fails, and only then bring in the expensive analysis for the survivors. Write the assumptions in the same file as the result, and future arguments take minutes instead of meetings.
Re-running this page costs nothing and catches the slow drifts that never announce themselves. In Business & Entrepreneurship the expensive mistakes are rarely sudden; they are small changes in Baseline rate (%) that nobody recalculated for a year. The point of transparency is that a reader can disagree with a specific line rather than with you.
The questions that come up most about Minimum Detectable Effect
What affects Minimum Detectable Effect the most?
Measured on this engine, Confidence level is the dominant lever: moving it ±10 % shifts the minimum detectable effect across 0.57 pts to 0.79 pts — about 27.2 % of the headline, with Statistical power next at ≈12.9 %. The ranked list in the sensitivity section is computed live, not asserted from a template.
Which matters more: statistical power or confidence level?
For Minimum Detectable Effect, Confidence level wins the head-to-head (≈27.2 % against ≈12.9 % per ten-percent change). Knowing which input dominates is the difference between careful work and merely slow work.
What is a typical Minimum Detectable Effect?
On the worked example above Minimum Detectable Effect comes out at 0.79 pts. Treat that as one point on a distribution rather than a norm: the bands, the companion outputs and the sensitivity ranking tell you how wide the plausible range really is.
How do I calculate Minimum Detectable Effect by hand?
MDE = (z_conf + z_power) × √(2p(1−p)/n) is the entire method. Work the inputs in that order — MDE = (2.58 + 0.84) × √(2×0.0400×0.9600 ÷ 14437) — and you will reach 0.79 pts on the default figures, the same number this tool prints.
What happens to Minimum Detectable Effect if confidence level changes by 10 %?
On these inputs a ±10 % change in confidence level takes Minimum Detectable Effect to 0.79 pts against the 0.79 pts example — around 27.2 % of the headline. The same test on every other field is in the sensitivity section.
Is the Minimum Detectable Effect result of 0.79 pts good or bad?
The tool answers “what”, not “whether”: 0.79 pts carries the verdict “Your test proves lifts ≥ 0.79 pts (19.7% relative) — anything smaller passes invisibly” for the default case, which is a starting interpretation rather than a verdict on your situation. Re-run with your own figures and compare the bands.
Can Minimum Detectable Effect be negative or empty?
Yes, and that is informative rather than broken: a negative Minimum Detectable Effect usually means the inputs encode an outflow or a shortfall, and the verdict band above labels exactly that situation instead of hiding it.
How do I calculate Minimum Detectable Effect manually?
Write down the inputs, then follow the printed steps in order — MDE = (z_conf + z_power) × √(2p(1−p)/n). A spreadsheet replicates it with two or three cells. The manual route is worth doing once to build intuition; after that the calculator saves time and eliminates transcription slips.
Should I power on revenue or conversion?
On whichever decision you will act; conversion gives 10× the events, so usually power on it and treat revenue as a guardrail read.
Do variance-reduction tricks shrink the MDE?
Yes — CUPED/covariate adjustment cuts effective variance 20–40% in mature setups, tightening the detectable band without new traffic.
Can this tool see the numbers I type?
It cannot. There is no submission step: the calculation happens in your browser and the result disappears when you close the page. Treat the fields above as a scratchpad rather than a form.
Key terms on this page
- As relative lift over baseline
- 19.7 % in the default Minimum Detectable Effect calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- n per arm to halve the MDE
- 57,748.0 in the default Minimum Detectable Effect calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- MDE at 99% confidence instead
- 0.79 pts for the Minimum Detectable Effect worked case; it sits next to the main result because it carries context the headline leaves out.
- Minimum detectable effect
- The primary output of this tool: 0.79 pts for the default inputs, computed exactly from MDE = (z_conf + z_power) × √(2p(1−p)/n).
- Worked example
- Every substitution in order, from the example inputs to 0.79 pts — the audit trail for the headline figure.
- Verdict band
- A named zone on the range of plausible results; the example inputs land in “Your test proves lifts ≥ 0.79 pts (19.7% relative) — anything smaller passes invisibly”, and your inputs may not.
- Sensitivity (±10 %)
- How far the Minimum Detectable Effect moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Where the Minimum Detectable Effect model comes from
The model is published arithmetic implemented exactly as written: MDE = (z_conf + z_power) × √(2p(1−p)/n). Source of record: Experimental-design arithmetic (MDE form). Any other implementation of this model should return the same figure for the same inputs. If one does not, the difference is in its assumptions — which this page prints and that one probably does not.
This page is an estimation aid, not professional advice. The design rule is simple: two people entering identical figures must get identical answers. The design constraint was set by usefulness rather than by comfort: an estimate you can interrogate beats an answer you have to trust.
After the number: what to do with it
Save the number together with its inputs and today’s date; a Minimum Detectable Effect figure without context is unusable the moment an input changes.
This page was written for people who need one trustworthy number before their next decision, and the promise is that nothing above required trust. Bookmark the tool, re-run it whenever an input moves by more than a few percent, and keep the date with the number.