Relative Risk Calculator
The cohort measure: risks straight from the table, their ratio with a log-scale interval, the absolute risk difference and relative risk reduction beside — with the protective direction named when the ratio drops below 1.
Relative Risk Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Cohort/RCT tables only — case-control margins make risks meaningless
- Zero events in the unexposed arm refuses the log method (boundary named)
In short: Cohort table a = 25, b = 75, c = 40, d = 60: the risk among the exposed is 25/100 = 0.25, among the unexposed 40/100 = 0.40, so the relative risk is 0.625 — exposure CUTS the risk to 62.5% of control, and the interval (0.412395, 0.947212) sits entirely below 1: protective, with the whole span agreeing. The absolute view: risk difference −0.15 (15 percentage points fewer events), relative risk reduction 0.375 — exposure prevents 37.5% of the risk. Relative answers how MANY TIMES; absolute answers how MANY — both are printed because a treatment that halves a risk from 2-in-a-million to 1-in-a-million still halves it.
Formula
RR = [a/(a+b)] ÷ [c/(c+d)] · SE(ln RR) = √(1/a − 1/(a+b) + 1/c − 1/(c+d))
The SE differs from the OR’s Woolf formula because risks — not odds — are being logged; both intervals are normal on the log scale and exponentiated back.
Worked Example
- Fill the four cohort cells: exposed and unexposed arms, outcome counts first.
- Read the two risks, then their ratio with the interval.
- Check the direction card: above 1 harms, below 1 protects — named, not implied.
- Read the absolute view before any headline: the ARR is what the Number Needed To Treat page spends.
Defaults: risks 0.25 and 0.40, RR 0.625, interval (0.412395, 0.947212) — entirely below 1, protective. ARR −0.15, RRR 0.375. Zero events in the unexposed arm refuses the log method by name.
Strengths & Limits Of This Model
Where this engine is strong
- Both scales printed: the ratio AND the absolute difference
- Direction named on its own card instead of implied by arithmetic
Where it stops
- No continuity correction for sparse cohort tables
- No adjustment for confounding — one 2×2 at a time
Practical Use Cases
Clinical
event rate in treated vs control arms
Safety
exposure group vs comparison group
Product
churn in variant A vs variant B
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Relative Risk Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
What is the difference between this and the odds ratio?
Different ratio, different license. This page divides RISKS (0.25/0.40); the odds page divides ODDS (0.25/0.75 over 0.40/0.60). They agree when the outcome is rare and diverge as it grows common. The deeper split is design: cohort data license the RR directly; case-control data license only the OR. Quote the one your design bought.
Why is the interval asymmetric?
It is built on the log scale — ln RR ± 1.959964×SE — and exponentiated back. On the log scale the ratio is symmetric around its estimate; after exponentiation the span is stretched further above than below, which is the honest shape for a quantity bounded at 0 and unbounded above.
RR = 0.625 — protective or harmful?
Protective: the exposed arm’s risk is 62.5% of the unexposed risk. Direction is named on its own card because “below 1” flips meaning with which arm you call exposed — the page fixes the reading to the table order you typed.
What is the absolute view adding?
The risk difference (−0.15) and the relative risk reduction (0.375). Ratios answer HOW MANY TIMES; differences answer HOW MANY. A drug that halves a 2-in-10,000 risk to 1-in-10,000 posts RR 0.5 — dramatic — and an ARR of 0.0001, which is the number the NNT page turns into “10,000 treated per event prevented”.
What if the unexposed arm had zero events?
The risk ratio would divide by zero — the page refuses the log method by name rather than printing a decimal for a division by zero. With zero unexposed events the honest report is the raw risks and their difference; the OR page’s +0.5 correction exists for ratios, and even it declares itself when it fires.
Can I use this for a case-control study?
No — and this is the one place the measure itself is invalid rather than merely less intuitive. Case-control sampling fixes the margins, so the risks 0.25 and 0.40 would be artifacts of how many cases the researchers chose to enroll. The odds ratio is the design’s only valid summary; this page hands that question off.
Why does the SE formula differ from the OR page’s?
Because the quantity being logged differs. The Woolf SE (1/a + 1/b + 1/c + 1/d) belongs to odds; the risk SE (1/a − 1/(a+b) + 1/c − 1/(c+d)) belongs to risks — the arm totals enter because a risk is a count over an arm. Same normal-on-the-log-scale machinery, different variance.
The interval crosses 1 — what do I say?
That the data are consistent with no effect: any claim of protection or harm is Licensing the world inside the interval where the ratio is exactly 1. Widen the study, not the claim — interval width shrinks with sample size like 1/√n, the same law every interval on this site obeys.