Effect Size (f) Calculator
The formula
What the cohen's f tells you
The effect size for ANOVA: standard-deviation-of-means scaled by residual SD, converted here from the more commonly reported η².
Calculation: Cohen's f = √(η² ∕ (1 − η²)); λ = f²·N; power from non-central F. Enter your inputs and every substitution is shown below the result.
Reading the result
η² of 6% across three groups (f ≈ 0.25) is a medium effect — real but demanding of sample to detect.
Rules of thumb: 0.10 / 0.25 / 0.40 = small / medium / large f
Limitations and best practice
η² in a fixed-design sample overstates the population effect; for planning use partial η² or ω²-adjusted values.
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
f vs η² — report which?
Does f work for repeated measures?
Source & methodology
Cohen (1988) ANOVA effect-size conventions.
Effect Size (f): the number, the method and the caveats
This page was written for one job: turning your own inputs into a defensible figure, with the working shown. Effect Size (f) is the kind of number people argue about from memory. This page ends that argument with arithmetic you can watch happen: enter your figures, get Cohen's f in real time, and see every substitution printed below.
Like most useful measures, Effect Size (f) is a summary, and summaries hide as much as they reveal. The companion outputs and the input table are here to reopen what the headline compressed.
A calculation like this one is worth roughly as much as a careful sentence: it forces several vague considerations into one comparable quantity. Once Effect Size (f) is on the table, the argument can stop being about impressions.
Nothing below is stock text pasted around a number: the worked example computes cohen's f = 0.253 from this tool’s own defaults, and the sensitivity section ranks the inputs that move the result — Variance explained η² first, at ≈5.4 % of the headline for a ten-percent error either way in that input — which is the thread the rest of this guide pulls on.
The Effect Size (f) formula, explained
The engine implements a single stated model: Cohen's f = √(η² ∕ (1 − η²)); λ = f²·N; power from non-central F. 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.
Variance explained η² (%) (example value 6) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Rates are the most mis-transcribed input on any page like this; copy it from the document rather than retyping from memory.
Number of groups (example value 3) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Count from the record, not the estimate; whole-number inputs are cheap to verify and expensive to get wrong.
Total sample (example value 98) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Replace the example with the figure from your own records — the tool recomputes instantly and the printed steps follow your numbers.
Effect Size (f) with real numbers, step by step
Abstract formulas are hard to trust, so here is the complete substitution using the default inputs, written the way an examiner would want it. Starting figures: Variance explained η² (%), Number of groups, Total sample. The endpoint of that chain is 0.253 of cohen's f, sitting in the “Large effect — the omnibus test will catch it” band.
- f = √(0.060 ÷ 0.940) = 0.253
- Ladder: f = 0.10 small · 0.25 medium · 0.40 large (variance-analytic effects)
η² as fraction — 0.060. Compare it against the main result of 0.253 before drawing conclusions.
Non-centrality λ = f²N — 6.26. Read next to the headline, this is the figure that shows the shape of the trade-off.
Approximate power at α=.05 — 92.8 %. This is the number experienced users quote when the headline alone would mislead.
n needed for 80% power — 252. If your inputs change, this is usually the first companion figure to move.
Keep this worked example open while you enter your own figures: matching the shape of the substitution is the fastest way to spot a unit or convention mistake.
The Effect Size (f) 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?
| Variance explained η² setting | Cohen's f |
|---|---|
| 80 % of the example value | 0.225 |
| 90 % of the example value | 0.239 |
| example inputs | 0.253 |
| 110 % of the example value | 0.266 |
| 120 % of the example value | 0.279 |
Across 5 settings of Variance explained η², the result spans 0.225 to 0.279. A decision that only works at one row of this table is a decision waiting for an input to move. Reproduce it in the form above by editing Variance explained η² alone; the substitution steps will follow your figures exactly.
What actually moves your Effect Size (f)
This list was computed for this specific engine just now: each numeric input was nudged ±10 % while every other field held its example value, and the cohen's f was recalculated from scratch. It is the fastest honest answer to “what matters most in Effect Size (f)?” — and it is specific to these defaults, because sensitivity moves with the starting point.
- Nudge Variance explained η² by ±10 % and Effect Size (f) lands between 0.239 and 0.266 (sensitivity ≈5.4 %)
Variance explained η² is the dominant lever here: ten percent either way moves the result by about 5.4 %, from 0.239 to 0.266. That is where a careless figure does the most damage, so check it against a source. The rest of the inputs earn only a rounding-error of attention, and that asymmetry is the practical payoff of measuring rather than asserting.
Interpreting the Effect Size (f) verdict
A number on its own is trivia; a number against a range is intelligence. The default case lands in the “Large effect — the omnibus test will catch it” band, and bands are deliberately wide because real situations overlap. The sensitivity list shows how far a modest input error moves you along that ladder: for Variance explained η², ±10 % covers 0.239 to 0.266. The practical reading rules: ask what would have to change to move you one band. If the answer is “a small, plausible input difference”, the band itself is not the finding — the uncertainty is.
The comparison worth making is not with somebody else’s Effect Size (f) but with the version of your own situation measured last quarter — same formula, same conventions, different inputs.
The errors that quietly break an Effect Size (f) figure
Η² in a fixed-design sample overstates the population effect; for planning use partial η² or ω²-adjusted values. 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.
Copying a single headline number without checking the companion outputs. The tool reports η² as fraction, Non-centrality λ = f²N and Approximate power at α=.05 alongside the main result precisely because Effect Size (f) in isolation misleads — the secondary columns are where outliers and trade-offs show up.
This model has its own particular trap: Variance explained η² carries ≈5.4 % of the response per ten percent of error, so effort spent elsewhere is largely decorative.
Another is comparing across contexts: an Effect Size (f) 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 Effect Size (f) figure
- Compare the output against one published benchmark or a colleague’s independent estimate.
- Confirm the example values are plausible for your own situation before replacing them.
- Check Variance explained η² before anything else: it is the measured dominant input, ≈5.4 % of Effect Size (f) per ten percent.
- Note the date and the inputs beside the number so the figure can be audited later.
- State, in one sentence, which convention each rate, unit or period in the form is using.
- Repeat the ±10 % test on the inputs that matter and see whether the decision — not just the number — still holds.
Step by step: getting a trustworthy Effect Size (f) 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 Effect Size (f) takes a minute to learn and applies to every input above.
Step 1 — collect, then type. Everything this tool asks for is listed above (variance explained η² (%), number of groups, total sample). Pull each figure from something you can point at — paperwork, a dashboard, a label — before touching a field. Guesswork at the input stage cannot be repaired at the interpretation stage. Note the assumption you are least sure about; that is where the real risk lives.
Step 2 — baseline before exploration. Get one defensible Cohen's f on screen before you start nudging numbers. Without a baseline, every variation looks interesting and none of them means anything. A calculation you cannot explain to somebody else is a calculation you cannot defend.
Step 3 — isolate your variables. Change one field, observe, revert. The live sensitivity list does the ranking for the default inputs; verify it against your own, because dominance shifts when the starting point shifts. The fastest sanity test is to guess the answer first and see how far the calculation disagrees.
Step 4 — compute a corridor, not a point. Three runs — worst, likely, best — turn Effect Size (f) from a snapshot into a range. Plan against the pessimistic end and treat the optimistic end as the upside story. Numbers are cheap to produce and expensive to retract; the extra minute is the cheapest insurance available.
Step 5 — record the context, not just the number. Note today’s date and the inputs alongside the 0.253 output. Six months from now the context is what turns this figure into a trend. When in doubt, prefer the boring input: the interesting one is usually the one you misread.
The real-world conversations Effect Size (f) settles
Most Statistics & Data Science disagreements are arithmetic disagreements in disguise. When Cohen's f of 0.253 sits on the table with its working shown, the conversation stops being about who sounds more confident and starts being about which input is wrong. Re-running a number costs seconds; retracting a decision costs considerably more.
Professionals in Statistics & Data Science use this style of calculation as a screening filter before spending real money or effort: a quick Effect Size (f) check eliminates weak options in minutes, and the survivors earn the deeper, slower analysis. Half of a good calculation is knowing which input you would hate to be wrong about.
Nothing here is stored or transmitted, so the habit of checking is free: open the page, re-enter current figures, compare with the number you saved last time. Comparisons are cheap: run the identical calculation for the alternative and look at the gap.
Quick answers: what searchers ask about Effect Size (f)
What affects Effect Size (f) the most?
Effect Size (f) is driven above all by Variance explained η². Perturbing only that field by ten percent either way produced 0.266 against the 0.253 baseline — a ≈5.4 % response.
What is a typical Effect Size (f)?
With the example inputs on this page the result is 0.253, labelled “Large effect — the omnibus test will catch it”. “Typical” varies with situation, which is why every result here ships with its verdict band and its sensitivity list: they turn one figure into a range you can locate yourself inside.
How do I calculate Effect Size (f) by hand?
Cohen's f = √(η² ∕ (1 − η²)); λ = f²·N; power from non-central F is the entire method. Work the inputs in that order — f = √(0.060 ÷ 0.940) = 0.253 — and you will reach 0.253 on the default figures, the same number this tool prints.
What happens to Effect Size (f) if variance explained η² changes by 10 %?
On these inputs a ±10 % change in variance explained η² takes Effect Size (f) to 0.266 against the 0.253 example — around 5.4 % of the headline. The same test on every other field is in the sensitivity section.
Is the Effect Size (f) result of 0.253 good or bad?
Good and bad are comparisons, so the honest test is three questions: where does your own Effect Size (f) sit against the 0.253 reference above, how far would a plausible input error move it (≈5.4 % per ten percent on Variance explained η²), and what does the alternative option compute to?
How many significant figures are reliable in Effect Size (f)?
About as many as your least precise input. The tool computes at full precision and displays rounded output; report 0.253 to a decimal place your inputs can actually support.
What affects Effect Size (f) the most?
Sensitivity depends on where you start, but the inputs Variance explained η² (%) and Number of groups typically move Effect Size (f) further than the rest because they enter the formula multiplicatively. If you can only measure two things well, measure those and hold the others at conservative defaults.
f vs η² — report which?
journals increasingly want η² or ω² with CIs; f is the power-calculation currency. Both, honestly labeled, is best.
Does f work for repeated measures?
Yes with within-subject error SDs — f grows when the same people carry all conditions.
Do I need an account to use this Effect Size (f) calculator?
No, and no data leaves the tab. The engine runs in the page itself, which is why the worked example, the bands and the sensitivity ranking all respond instantly to your keystrokes.
The vocabulary of Effect Size (f)
- η² as fraction
- 0.060 for the Effect Size (f) worked case; it sits next to the main result because it carries context the headline leaves out.
- Non-centrality λ = f²N
- 6.26 in the default Effect Size (f) calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Approximate power at α=.05
- 92.8 % on the example inputs — a companion figure printed beside the headline of Effect Size (f) so that no result is read in isolation.
- Cohen's f
- The primary output of this tool: 0.253 for the default inputs, computed exactly from Cohen's f = √(η² ∕ (1 − η²)); λ = f²·N; power from non-central F.
- Worked example
- The step-by-step substitution printed above, so the arithmetic can be re-derived by hand or in a spreadsheet.
- Verdict band
- The interpretation attached to a result (“Large effect — the omnibus test will catch it” on these inputs), which turns a bare number into a position on a scale.
- Sensitivity (±10 %)
- How far the Effect Size (f) moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Methodology, sources and limits
The model is published arithmetic implemented exactly as written: Cohen's f = √(η² ∕ (1 − η²)); λ = f²·N; power from non-central F. Source of record: Cohen (1988) ANOVA effect-size conventions. 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.
Nothing here replaces a qualified professional, and nothing here is approximate either — the arithmetic is exact, and the honesty is in the inputs you supply. The promise to the reader is narrow and testable: same inputs, same output, no silent rounding, and no figure presented without the formula that produced it.
What to do with your Effect Size (f) next
Save the number together with its inputs and today’s date; an Effect Size (f) figure without context is unusable the moment an input changes.
Whoever you are (people who need one trustworthy number before their next decision), the next step is the same: replace the example inputs with your own, note the date, and re-run whenever a figure moves. In Science & Research, a dated figure is a trend, and an undated one is a rumour.