An odds ratio of 2 at a 40% baseline risk. The risk ratio is 1.4286 — exactly 10/7 — so the group with the exposure has a 57.14% chance against 40%, not an 80% chance. "Twice as likely" would be wrong by a wide margin, and this is the regime almost every published odds ratio about a common outcome sits in. The interval converts too: an odds ratio interval of 1.4 to 2.9 becomes a risk ratio interval of 1.2069 to 1.6477, which is narrower because the transformation compresses everything towards 1.
Odds ratio 2.0000 at a baseline risk of 40.00%
Risk ratio 1.4286 — 40.00% becomes 57.14%
The odds ratio's apparent effect is 2.33 times the risk ratio's. Reading 2.00 as a probability multiplier would put the exposed group at 80.00%, against the correct 57.14%.
Risk ratio
1.4286
odds ratio 2.0000
Risk if exposed
57.14%
baseline 40.00%
Absolute difference
17.14 pts
more likely
Overstatement
2.33×
odds ratio against risk ratio
The interval converts the same way, one endpoint at a time: an odds ratio interval of 1.400 to 2.900 becomes a risk ratio interval of 1.2069 to 1.6477. It is narrower on the risk scale because the transformation compresses everything towards 1 — and it inherits every assumption the original interval carried, including that the baseline risk you supplied is exact rather than estimated.
The same odds ratio at every baseline
How the risk ratio for this odds ratio changes with the baseline risk
Baseline risk
Risk ratio
Risk if exposed
Absolute change
Overstatement
1%
1.9802
1.98%
0.98 pts
1.02×
2%
1.9608
3.92%
1.92 pts
1.04×
5%
1.9048
9.52%
4.52 pts
1.11×
10%
1.8182
18.18%
8.18 pts
1.22×
20%
1.6667
33.33%
13.33 pts
1.50×
30%
1.5385
46.15%
16.15 pts
1.86×
40%
1.4286
57.14%
17.14 pts
2.33×
50%
1.3333
66.67%
16.67 pts
3.00×
60%
1.2500
75.00%
15.00 pts
4.00×
75%
1.1429
85.71%
10.71 pts
7.00×
90%
1.0526
94.74%
4.74 pts
19.00×
One odds ratio, eleven different risk ratios. This is why an odds ratio quoted without its baseline risk is not a reportable finding: the same number means a 1-point change at one baseline and a 20-point change at another.
Everything here is exact arithmetic with no estimation in it, so the verification suite checks it against values worked out by hand — an odds ratio of 2 at 40% is exactly 10/7 — and against the two limits: the risk ratio always lies between 1 and the odds ratio, and converges to the odds ratio as the baseline risk approaches zero.
The conversion assumes the odds ratio applies to the group whose baseline risk you entered. An odds ratio adjusted for covariates is conditional on them, and applying it to a marginal baseline risk mixes two different quantities — the answer is then indicative rather than exact.
Exact, not approximate Intervals convert too Every baseline shown Needs the right baseline
What this tool shows
An odds ratio of 2 is a risk ratio of 1.9608 at a 2% baseline risk and 1.2500 at a 60% one. Same odds ratio, and the difference between “almost twice as likely” and “a quarter more likely”. Odds ratios are what logistic regression and case-control studies produce; risks are what people hear. The conversion is exact arithmetic and needs one extra number — the baseline risk in the unexposed group — which is the number most often left out of the sentence.
The exact conversion RR = OR / (1 − p₀ + p₀·OR), at any baseline risk you name
The absolute risks on both sides, and the percentage-point difference between them
The confidence interval converted endpoint by endpoint
How much the odds ratio overstates the effect, as a factor
The same odds ratio across eleven baselines, from 1% to 90%
Where the rare-outcome approximation holds and where it stops holding
Exact, not approximate Intervals convert too Every baseline shown Checked by hand
The answer is only as good as the baseline risk you supply.
Updated 13 September 2026 · Works in any browser, no installation
A risk ratio is OR / (1 − p₀ + p₀·OR), where p₀ is the risk in the unexposed group. The odds ratio is always further from 1 than the risk ratio, on either side, and the gap grows with the baseline risk. They agree closely when the outcome is rare, which is the assumption that made odds ratios the default in case-control research and the assumption that fails whenever the outcome is common.
At a glance
Formula shown
RR = OR / (1 − p₀ + p₀·OR). At p₀ → 0 the denominator → 1 and RR → OR. At p₀ → 1 it → OR/OR = 1, so every odds ratio collapses to no effect at all — there is no room left above 100%. The risk in the exposed group is p₀·RR, and the absolute risk difference is p₀(RR − 1), which is usually the number a decision actually turns on.
Scenario support
Reading a published odds ratio from a logistic regression or case-control study, translating a model coefficient into something a patient or a stakeholder can act on, checking whether a headline “twice as likely” is supported, and converting an adjusted odds ratio into an approximate risk for a specific baseline group.
Educational estimate
Planning support from the values you enter — not professional advice.
One odds ratio, eleven answers
The table on this page shows the same odds ratio at every baseline from 1% to 90%, and that spread is the whole reason the conversion is needed.
An odds ratio of 2 at a 2% baseline is a risk ratio of 1.9608. Close enough that treating them as the same is defensible.
At 20% it is 1.6667; at 40%, 1.4286; at 60%, 1.2500. By the last of those, the “twice as likely” reading overstates the effect by a factor of four.
The absolute change tells the same story differently. At 2% the exposed group moves to 3.92% — two percentage points. At 40% it moves to 57.14% — seventeen.
Which is why an odds ratio without a baseline is not a finding. It is a transformation waiting for a number that turns it into one.
The error always runs the same way
The distortion is not random, which makes it easy to reason about once the direction is fixed in mind.
The odds ratio is always further from 1 than the risk ratio. On both sides — the verification suite asserts it on 150 random combinations.
So a harmful exposure always looks more harmful than it is, and a protective one always looks more protective.
On the third preset an odds ratio of 0.4 is a risk ratio of 0.5714: a 43% reduction, not the 60% the odds ratio suggests.
The mechanism is that odds are unbounded and risks are not. Odds run from 0 to infinity; risks stop at 1. As the baseline rises there is less and less room above it, and the odds ratio does not know that.
Where the rare-outcome approximation holds
The approximation is not wrong, it is conditional, and knowing where the condition bites is more useful than a warning.
At a 1% baseline an odds ratio of 2 is a risk ratio of 1.9802. A 1% error.
At 5% it is 1.9048 — a 5% error. At 10%, 1.8182, a 9% error. The error tracks the baseline closely for small odds ratios.
Large odds ratios break it sooner. An odds ratio of 10 at a 10% baseline is a risk ratio of 5.2632 — barely half.
The usual rule of thumb is a baseline below 10%, and it is only safe for modest odds ratios. The table on this page replaces the rule with the actual number, which is always better.
Why odds ratios exist at all
Given all of that, the reasonable question is why anyone reports odds ratios, and there are two good answers.
A case-control study cannot estimate risk. Cases and controls are sampled separately, so the observed proportion of cases carries no information about the underlying rate — but the odds ratio is invariant to that sampling, which is the whole reason the design works.
Logistic regression produces them by construction. It models log odds, so exponentiating a coefficient gives an odds ratio and nothing else.
They are also symmetric in a way risk ratios are not. The odds ratio for the outcome is the reciprocal of the odds ratio for its absence; risk ratios have no such property.
So the answer is not to stop reporting them. It is to report the baseline risk alongside — which turns the odds ratio into something that can be converted, checked, and acted on.
Adjusted odds ratios need more care
The conversion is exact for a crude odds ratio from a two-by-two table. For an adjusted one it is approximate, and the reason is worth knowing.
An adjusted odds ratio is conditional on the covariates. It describes the effect within strata of them, not across the whole population.
A marginal baseline risk is not conditional on anything. Combining the two mixes quantities defined on different populations.
The mismatch is called non-collapsibility, and it is a property of the odds ratio rather than an error in anyone’s method — an adjusted odds ratio can differ from the crude one even with no confounding at all.
In practice the conversion is still informative, as long as the baseline risk used is for the specific group being described rather than the study average, and the result is presented as indicative.
The absolute difference is usually the real answer
Both ratios are relative measures, and relative measures are the ones that mislead when the baseline is small.
A risk ratio of 2 on a baseline of 0.1% takes the risk to 0.2%. Double, and one person in a thousand.
The same ratio on a baseline of 30% takes it to 60%. Also double, and thirty people in a hundred.
The page prints the percentage-point change for that reason, beside both ratios.
Its reciprocal is the number needed to treat, which is the form most decisions actually turn on: how many people have to be exposed for one additional outcome to occur.
Reporting a converted ratio
Four items, and the first is the one whose absence started the problem.
Give the baseline risk you used, and where it came from. The conversion is only as good as that number, and a different one gives a different answer.
Give both ratios, not one. Replacing an odds ratio with a risk ratio silently changes what a reader can compare your result against.
Give the absolute risks. They are what makes a relative measure interpretable, and they cost nothing to include.
And say whether the odds ratio was adjusted. The conversion is exact for a crude odds ratio and approximate for an adjusted one, and that distinction belongs in the sentence.
Method. The conversion is Zhang and Yu’s exact expression RR = OR / (1 − p₀ + p₀·OR), applied to the point estimate and to each interval endpoint separately. There is no estimation in it, which means the verification suite can check it against values computed by hand rather than against a tolerance: an odds ratio of 2 at a 40% baseline must be exactly 10/7, and at 5% exactly 40/21. It also asserts the two limits that characterise the formula — the risk ratio always lies between 1 and the odds ratio, on either side, and converges to the odds ratio as the baseline risk approaches zero — each on 150 random combinations, along with the requirement that an odds ratio of 1 converts to a risk ratio of exactly 1 at every baseline and that a baseline outside the open unit interval returns nothing rather than a plausible number. That engine is verified on every change against 100 assertions. The count and the per-case breakdown are published on the formula verification page.
Related calculators
Where this goes next:
Logistic RegressionLogistic regression with odds ratios converted to risk ratios at your own event rate, a likelihood ratio test, AUC, and separation reported rather than hidden.
Relative RiskRisk ratio and odds ratio from one table with the divergence between them plotted: they agree to half a percent at a 1% baseline, and at an 80% baseline the odds ratio is exactly half the risk ratio.
Odds RatioOdds ratio, relative risk, risk difference and number needed to treat from one 2x2 table — because an odds ratio of 6.00 can describe a relative risk of 1.50.
Number Needed to TreatNNT from the absolute risk reduction, with the relative figure beside it — two trials reporting the identical “50% reduction” have NNTs of 7 and 1,000, and the common shortcut says 2 for both.
Sensitivity and SpecificitySensitivity, specificity, PPV, NPV, likelihood ratios and MCC from a 2×2 table, with predictive values recomputed across the prevalence range — a 99%/99% test has a PPV of 50% at 1% prevalence and 9% at 0.1%.
Hosmer-LemeshowThe Hosmer-Lemeshow calibration test with the group count swept from five to fifteen, per-group promised-against-observed rates, and the Brier reliability alongside.
An educational tool. The conversion is exact arithmetic, but the answer is only as good as the baseline risk supplied — that must be the risk in the unexposed or reference group, not the overall rate in a study. For an adjusted odds ratio the conversion is approximate, because an adjusted odds ratio is conditional on the covariates while a marginal baseline risk is not.