These measures are the language of clinical trials and epidemiology.
How to use the Relative Risk and Odds Ratio Calculator
- Exposed with outcome (a)
- Exposed without outcome (b)
- Unexposed with outcome (c)
- Unexposed without outcome (d)
Results update as you type, and every field accepts the units shown in its menu.
How it works
Risks are computed in each group from the table; the ratios and differences follow directly.
Inputs explained
| Field | What to enter |
|---|---|
| Exposed with outcome (a) | A number |
| Exposed without outcome (b) | A number |
| Unexposed with outcome (c) | A number |
| Unexposed without outcome (d) | A number |
What each result means
- Risk in exposed = [Exposed with outcome (a)]÷([Exposed with outcome (a)] + [Exposed without outcome (b)])×100
- Risk in unexposed = [Unexposed with outcome (c)]÷([Unexposed with outcome (c)] + [Unexposed without outcome (d)])×100
- Relative risk = [Risk in exposed]÷[Risk in unexposed]
- Odds ratio = [Exposed with outcome (a)]×[Unexposed without outcome (d)]÷([Exposed without outcome (b)]×[Unexposed with outcome (c)])
- Absolute risk difference = [Risk in exposed] – [Risk in unexposed]
- Number needed to treat/harm = 100÷abs([Absolute risk difference])
Example values
How the main result changes when Exposed with outcome changes and everything else stays at the example values above:
| Exposed with outcome (a) | Relative risk |
|---|---|
| 10 | 1.1111 |
| 15 | 1.5789 |
| 20 | 2 |
| 25 | 2.381 |
| 30 | 2.7273 |
| 40 | 3.3333 |
Formula
RR = (a ÷ (a + b)) ÷ (c ÷ (c + d))OR = (a × d) ÷ (b × c)NNT = 1 ÷ |risk difference|Worked example
Inputs — Exposed with outcome (a): 20; Exposed without outcome (b): 80; Unexposed with outcome (c): 10; Unexposed without outcome (d): 90.
Results — Risk in exposed = 20 %; Risk in unexposed = 10 %; Relative risk = 2; Odds ratio = 2.25; Absolute risk difference = 10 percentage points; Number needed to treat/harm = 10.
Frequently asked questions
When is the odds ratio close to the relative risk?
When the outcome is rare.
What does NNT = 10 mean?
Ten people need the treatment for one extra person to benefit.
What formula does the Relative Risk and Odds Ratio Calculator use?
RR = (a ÷ (a + b)) ÷ (c ÷ (c + d)).