Odds Ratio Calculator
Calculate Odds Ratio from 2x2 Contingency Table
Calculate
Clear
Odds Ratio Formula
Odds Ratio = (a×d)/(b×c)
ln(OR) = ln(a) + ln(d) - ln(b) - ln(c)
SE(ln(OR)) = √(1/a + 1/b + 1/c + 1/d)
If CI doesn't include 1, association is statistically significant!
⚠
Ensure a, b, c, d ≥ 1 for stable calculations (add 0.5 to each cell if any zero).
What is Odds Ratio?
Odds Ratio measures the association between an exposure and an outcome in a 2x2 contingency table.
Odds Ratio
Association measure
Confidence Interval
Precision estimate
OR > 1
Higher odds in exposed
OR < 1
Lower odds in exposed
💡 Example: a=20, b=80, c=10, d=90 → OR=(20×90)/(80×10)=2.25
Applications
Epidemiology
Medicine
Biostatistics
Public Health
Research
Frequently Asked Questions
What is odds ratio?▼
OR = (a/b)/(c/d) = (a×d)/(b×c). Measures association between exposure and outcome. OR=1 no association.
How to interpret odds ratio?▼
OR>1: exposure associated with higher odds. OR<1: lower odds. OR=1: no association. Consider magnitude and CI.
What is confidence interval for OR?▼
CI for ln(OR) = ln(OR) ± z×√(1/a+1/b+1/c+1/d). Exponentiate to get CI for OR.
Odds ratio vs risk ratio?▼
OR compares odds, RR compares risks. Similar when outcome rare; differ for common outcomes.
Free online calculators and tools covering mathematics, unit conversion, text processing, and daily life. Accurate, fast, mobile-friendly, and completely free to use.
© 2026 IP331.com — Free Online Tools. All rights reserved.
About
·
Contact
·
Privacy Policy
·
Cookie Policy
·
Terms of Use
·
Disclaimer
·
Sitemap