Statistics

Relative Risk Odds Ratio Calculator

Compute RR, OR, and confidence intervals from a 2x2 contingency table.

Last validated: 2026-02-14

Relative Risk Odds Ratio Calculator derives two common association measures from a 2x2 outcome table. Relative risk compares event probability in an exposed group with event probability in an unexposed group, making it natural for cohort studies and experiments where risks can be observed directly. Odds ratio compares event odds rather than event probabilities; it is widely used in case-control studies and logistic regression because odds remain computable when sampling starts from outcomes. When events are rare, the odds ratio and relative risk can be similar, but for common outcomes the odds ratio can look much larger. The four table cells represent exposed cases, exposed non-cases, unexposed cases, and unexposed non-cases, so correct table orientation is essential.

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Input Pattern

Enter values in the left panel, keep units explicit, run the calculation, then copy or share the result. Invalid fields are highlighted immediately.

2x2 Table Inputs

a=exposed+outcome, b=exposed+no outcome, c=unexposed+outcome, d=unexposed+no outcome

Result

Risk exposed: 0.450000

Risk unexposed: 0.200000

Relative risk: 2.25000000

RR 95% CI: 1.437687 to 3.521281

Odds ratio: 3.27272727

OR 95% CI: 1.745242 to 6.137109

How to use this tool

Enter a, b, c, d for the relative risk odds ratio calculator, keeping units, dates, or text format consistent with the form labels.
Confirm sample size, ordering, and distribution assumptions before relying on the calculated result.
Click "Run the tool" and review 2x2 Table Inputs, Result for the primary output.
Check the statistical assumptions and sample context before using the result in a report or decision.

Worked Example

Auto-generated from the tool's current default or entered inputs.

Example Inputs

A: 45
B: 55
C: 20
D: 80
Adjusted:
Risk exposed: 0.45
Risk unexposed: 0.2
Relative risk: 2.25

Expected Outputs

A: 45
B: 55
C: 20
D: 80

Interpretation

A is 45. Use this as a decision input, not as a standalone conclusion.
B is 55. Use this as a decision input, not as a standalone conclusion.
C is 20. Use this as a decision input, not as a standalone conclusion.
Interpret this value alongside sample quality and assumptions to avoid overconfidence.

Confidence and limitations

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Interpretation depends on assumptions (distribution, independence, sample quality).

Formula References

Frequentist estimation and hypothesis-test formulas used in standard textbooks.
Interpretation depends on sample quality and assumptions.

Assumptions

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Interpretation depends on assumptions (distribution, independence, sample quality).

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Relative Risk Odds Ratio Calculator

Input Pattern

2x2 Table Inputs

Result

How to use this tool

Worked Example

Example Inputs

Expected Outputs

Interpretation

Confidence and limitations

Formula References

Assumptions

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