SigmaCalc

Relative Risk Calculator

A direct comparison of event probability between two groups — the standard measure in cohort and clinical trial studies.

Exposed, with event (a)

Exposed, without event (b)

Unexposed, with event (c)

Unexposed, without event (d)

Relative risk

RR = [a÷(a+b)] ÷ [c÷(c+d)]

What you entered

Exposed, with event (a): 30Exposed, without event (b): 70Unexposed, with event (c): 10Unexposed, without event (d): 90

1
Risk of the event in the exposed group
30 ÷ (30 + 70)= 0.3
2
Risk of the event in the unexposed group
10 ÷ (10 + 90)= 0.1
3
Relative risk
0.3 ÷ 0.1= 3

Result

Relative risk: 3

A relative risk of 3 means the exposed group is 3× more likely to experience the event than the unexposed group.

Relative risk from a two-by-two table

Relative risk is the risk in the exposed group divided by the risk in the unexposed group, using the same a, b, c, d layout as the odds ratio.

a	b	c	d	Relative risk	Odds ratio
30	70	20	80	1.500	1.714
40	60	20	80	2.000	2.667
15	85	10	90	1.500	1.588
50	50	25	75	2.000	3.000

Relative risk is the more intuitive of the two: 2.000 means the exposed group has twice the risk, full stop. But it is only valid when you can measure risk directly, which means a cohort or trial design - in a case-control study the sampling fixes the number of cases, so risk cannot be estimated and the odds ratio is the correct measure. Note also that a relative risk of 2 says nothing about the absolute change: a doubling from 1 in a million to 2 in a million is very different from 10% to 20%, and the absolute risk difference is what usually matters for a decision.

Relative risk needs the right study design

Unlike odds ratio, relative risk requires knowing the true incidence in each group — which means it's appropriate for cohort studies and clinical trials, but generally not for case-control studies where the sampling itself is based on outcome status.

Reading the number

A relative risk of 1 means equal risk between groups. A relative risk of 2 means the exposed group is twice as likely to experience the event; 0.5 means half as likely — it's a direct, intuitive ratio of probabilities.

Frequently asked questions

A vaccine trial: 10 of 5,000 vaccinated got sick vs 50 of 5,000 unvaccinated. How effective is it?

RR = (10/5000) / (50/5000) = 0.002/0.01 = 0.20. Vaccine efficacy = 1 − RR = 1 − 0.20 = 80%. The vaccine reduces the risk of getting sick by 80% — the vaccinated group was 5× less likely to get sick.

When should I use relative risk vs odds ratio?

Use RR for cohort studies and clinical trials (where you follow groups forward in time and can calculate actual incidence rates). Use OR for case-control studies (where you start with outcomes and look backward). See the odds ratio calculator for case-control studies.

What is absolute risk reduction?

ARR = risk in control − risk in treated. In the vaccine example: 1.0% − 0.2% = 0.8%. Number needed to treat (NNT) = 1/ARR = 125 — you need to vaccinate 125 people to prevent one case. ARR gives a more practical sense of impact than relative risk alone.