Relative risk and NNT: aspirin and heart attack
A randomized trial comparing heart attacks in aspirin and placebo groups.
Odds Ratio Calculator
FigranEnter a 2×2 table to get the odds ratio, relative risk and NNT with confidence intervals and exact tests.
- OR, RR, risk difference and NNT
- Fisher exact and chi-square
- Exact CIs for small or zero cells
Data
Total
Total
Options
OR = 0.58
95% CI 0.47 to 0.71 · RR 0.58 · NNTB 111 · Chi-square p < 0.0001
Results
| Measure | Estimate | Confidence interval | Method |
|---|---|---|---|
| Odds ratio | 0.58 | 0.47 to 0.71 | Woolf |
| Conditional exact OR | 0.58 | 0.46 to 0.71 | Exact (conditional) |
| Relative risk | 0.58 | 0.47 to 0.72 | Katz |
| Relative risk reduction | 41.9% | 28.5% to 52.7% | Katz |
| Risk difference | −0.91 percentage points | −1.25 to −0.57 | Newcombe |
| Number needed to treat | NNTB 111 | NNTB 80 to 177 | 1 / |RD| |
| Event risk: Aspirin | 1.3% | 1.1% to 1.5% | Wilson |
| Event risk: Placebo | 2.2% | 1.9% to 2.5% | Wilson |
Tests
Minimum expected count: 188.97
| Test | Statistic | Degrees of freedom | p value |
|---|---|---|---|
| Fisher: two-sided | — | — | p < 0.0001 |
| Chi-square | 26.9 | 1 | p < 0.0001 |
| Chi-square (Yates) | 26.4 | 1 | p < 0.0001 |
Observed / expected
| Name | Heart attack | No heart attack | Total |
|---|---|---|---|
| Aspirin | 139 / 189.03 | 10,898 / 10,847.97 | 11,037 |
| Placebo | 239 / 188.97 | 10,795 / 10,845.03 | 11,034 |
| Total | 378 | 21,693 | 22,071 |
Report
Results
Heart attack occurred in Aspirin (139 of 11,037, 1.3%) and in Placebo (239 of 11,034, 2.2%). OR 0.58 (95% CI 0.47 to 0.71); RR 0.58 (95% CI 0.47 to 0.72); Chi-square p < .0001. Risk difference −0.91 percentage points, 95% CI −1.25 to −0.57; NNTB 111 (NNTB 80 to 177).
Methods
Odds ratios with 95% confidence intervals were calculated using the Woolf method. Relative risks used Katz intervals and risk differences used Newcombe intervals. Groups were compared using the chi-square test.
Odds ratio calculator examples
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Mantel–Haenszel odds ratio: birth weight by race
Compare crude and adjusted odds ratios across three strata.
Simpson’s paradox: Berkeley graduate admissions
Compare crude and department-adjusted odds ratios.
How to calculate an odds ratio
Enter your counts, choose a method and export the results.
1Choose a design
Select cohort or trial, or case–control.
2Enter counts
Fill the 2×2 table or enter events and totals.
3Review the results
Compare the estimates, intervals and tests.
4Export
Download a figure or copy a report.
Odds ratio, relative risk or NNT?
Choose an estimate that fits the way the data were collected.
| Design | Measures | Default interval | Notes |
|---|---|---|---|
| Case–control | OR only | Woolf | Sampling fixes case and control totals. |
| Cohort or trial | OR, RR, RD, NNT | Woolf, Katz, Newcombe | Risk estimates require defined groups and follow-up. |
| Cross-sectional | OR, RR | Woolf, Katz | RR is a prevalence ratio. |
When the odds ratio overstates the relative risk
When an outcome is common, an odds ratio can lie farther from 1 than the risk ratio. In the birth-weight example, OR is 2.02 and RR is 1.61.
Fisher’s exact test or chi-square?
Auto selects Fisher when any expected count is below 5, and Pearson chi-square otherwise. The selected test is named with the result.
Zero cells
Adding 0.5 to all four cells supports Woolf and Katz intervals. Fisher and conditional exact intervals use the original counts.
Adjusting for a confounder
Use strata to compare a crude odds ratio with a Mantel–Haenszel estimate. The Breslow–Day test examines variation among strata.
References: Zhang & Yu (1998) · Cochran (1954) · Haldane (1956) · Mantel & Haenszel (1959) · Breslow & Day (1980)
Odds ratio formulas and confidence intervals
For a table with cells a, b, c and d, the estimators are:
Odds ratio
OR = (a × d) / (b × c)
OR = 139 × 10,795 / (10,898 × 239) = 0.58
SE(log OR) = √(1/a + 1/b + 1/c + 1/d)
Relative risk
RR = [a / (a + b)] / [c / (c + d)]
SE(log RR) = √[1/a − 1/(a + b) + 1/c − 1/(c + d)]
Risk difference
RD = a / (a + b) − c / (c + d)
NNT = 1 / |RD|
Newcombe combines Wilson intervals for the two risks; NNT is the reciprocal of the absolute risk difference.
Tests
χ² = Σ (O − E)² / E
P(a) = C(a + b, a) C(c + d, c) / C(n, a + c)
Mantel–Haenszel odds ratio
ORMH = Σ(aᵢdᵢ/nᵢ) / Σ(bᵢcᵢ/nᵢ)
References: Woolf (1955) · Katz et al. (1978) · Newcombe (1998) · Altman (1998) · Fisher (1935) · Robins, Breslow & Greenland (1986)
Odds ratio calculator FAQ
How do I calculate an odds ratio from a 2×2 table?
Multiply a by d and divide by b times c. A Woolf confidence interval uses the logarithm of the odds ratio.
What is the difference between an odds ratio and relative risk?
Relative risk compares probabilities; an odds ratio compares odds. For common outcomes, the odds ratio is often farther from 1.
How do I interpret an odds ratio and its 95% CI?
An OR above 1 indicates higher odds in the first group; an OR below 1 indicates lower odds. A wide interval indicates substantial uncertainty. To convert an odds ratio to Cohen’s d, use the effect size calculator.
When should I use Fisher’s exact test instead of chi-square?
Fisher’s test is useful for small expected counts. Auto selects it when any expected count is below 5.
What if one cell is zero?
A 0.5 correction can support Woolf and Katz intervals; exact methods use the original counts. If neither group has events, OR and RR are not estimable.
How is the number needed to treat calculated?
NNT is the reciprocal of the absolute risk difference, rounded up. A confidence interval crossing zero extends through infinity between benefit and harm.
Can I adjust the odds ratio for a confounder?
Yes. Enter strata to calculate a Mantel–Haenszel odds ratio; multiple covariates require a regression model.
Which 2×2 tables does this calculator not handle?
Diagnostic tables use sensitivity and specificity; pooling studies uses a forest plot; survival times use a Kaplan–Meier analysis. Paired data need McNemar’s test, tables larger than 2×2 need r×c methods, and prospective sample size needs power analysis. Related tools: sensitivity and specificity calculator · forest plot generator · Kaplan–Meier curve generator · power analysis calculator.
Do the results match R, MedCalc, OpenEpi, SPSS and Stata?
Methods and defaults differ across statistical packages. The conditional exact interval inverts Fisher’s noncentral hypergeometric distribution using high-precision root solving; R fisher.test uses a default solver tolerance, so results can differ in later significant digits. Counts stay in your browser. Woolf uses a large-sample approximation; exact intervals are useful with small or zero cells, while mid-p intervals are less conservative.
Analyse your 2×2 table
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