STATISTICSProbability TheoryStatistics Calculator
📊

Relative Risk Calculator

Free relative risk calculator. Compute RR, ARR, NNT, RRR, and confidence intervals from 2×2 continge

Run CalculatorExplore data analysis and statistical calculations

Why This Statistical Analysis Matters

Why: Statistical calculator for analysis.

How: Enter inputs and compute results.

📊
EPIDEMIOLOGYRisk ratio, ARR, NNT, CI from 2×2 tables

Relative Risk: RR, ARR, NNT from 2×2 Tables

From clinical trials to public health — RR, ARR, and NNT communicate effect size. Master the 2×2 table.

Risk Calculator →Odds Ratio →

Real-World Scenarios — Click to Load

2×2 Table Inputs

Event in exposed group
No event in exposed
Event in control
No event in control
relative-risk.sh
CALCULATED
$ relative_risk --table a=30 b=70 c=10 d=90
Relative Risk
3.000
95% CI: 1.551 – 5.803
EER
30.00%
CER
10.00%
ARR
20.00%
NNT/NNH
5.0
RRR
66.67%

2×2 Table

EventNo EventTotal
Exposed3070100
Unexposed1090100
Share:
Relative Risk Result
RR = 3.000
95% CI: [1.551, 5.803]
ARR: 20.00%NNT: 5.0RRR: 66.67%
numbervibe.com/calculators/statistics/relative-risk-calculator

Calculation Breakdown

COMPUTATION
EER (Exposed Event Rate)
30.00%
a/(a+b) = 30/100
COMPUTATION
CER (Control Event Rate)
10.00%
c/(c+d) = 10/100
RESULT
Relative Risk
3.0000
EER/CER = 0.3000/0.1000
RESULT
Absolute Risk Reduction
20.00%
ext{EER} - ext{CER}
RESULT
NNT/NNH
5.0
1/| ext{ARR}|
CONFIDENCE INTERVAL
95% CI for RR
[1.551, 5.803]
\text{exp}(\text{ln}( ext{RR}) pm z imes ext{SE})

Risk Comparison (EER vs CER)

RR Forest Plot Style

Effect Size Summary

For educational and informational purposes only. Verify with a qualified professional.

Key Takeaways

  • • Relative Risk (RR) compares risk in exposed vs unexposed groups; RR > 1 means exposure increases risk
  • • RR is preferred over Odds Ratio for prospective studies when outcome is common
  • • Absolute Risk Reduction (ARR) and NNT communicate clinical impact better than RR alone
  • • Confidence intervals for RR are computed on the log scale then exponentiated
  • • NNT = 1/|ARR| tells you how many people need treatment to prevent (or cause) one event

Did You Know?

🩺RR is the primary effect measure in cohort studies and randomized trialsSource: Cochrane Handbook
📊A vaccine with RR=0.1 means 90% relative risk reductionSource: Vaccine efficacy
⚖️When outcome is rare (<10%), OR approximates RRSource: Epidemiology
🏥NNT of 5 means treat 5 people to prevent one bad outcomeSource: Clinical trials
📈RR > 1: harmful exposure; RR < 1: protective; RR = 1: no associationSource: Standard interpretation
🔬The Woolf method for RR CI assumes large samplesSource: Statistical methods

Expert Tips

Use RR for prospective studies

Cohort studies and RCTs: RR is directly interpretable. Case-control: use OR.

Report both RR and ARR

RR can exaggerate small absolute differences. ARR and NNT give clinical context.

Check CI for significance

If 95% CI includes 1, the association is not statistically significant at α=0.05.

NNH for harmful exposures

When RR > 1, NNH = 1/ARR tells how many exposed to observe one extra event.

RR vs Odds Ratio

AspectRelative RiskOdds Ratio
Study designCohort, RCTCase-control, cross-sectional
InterpretationRisk ratioOdds ratio
When outcome rare≈ OROR exact
When outcome commonRR preferredOR overestimates RR
FormulaEER/CER(a/c)/(b/d)

Frequently Asked Questions

What is the difference between RR and OR?

RR = risk in exposed / risk in unexposed. OR = odds in exposed / odds in unexposed. For rare outcomes they are similar; for common outcomes RR is more interpretable.

When should I use RR?

Use RR for cohort studies, randomized trials, and prospective designs where you can estimate incidence in both groups.

What does NNT mean?

Number Needed to Treat: how many people need to receive the treatment to prevent one additional event. NNT = 1/|ARR|.

Why is the CI computed on ln(RR)?

RR is bounded below by 0 but unbounded above. The sampling distribution of ln(RR) is approximately normal.

What is RRR?

Relative Risk Reduction = 1 − RR when RR < 1 (protective). E.g., RR=0.5 means RRR=50%.

Can RR be greater than 1?

Yes. RR > 1 means exposure increases risk. RR < 1 means exposure reduces risk. RR = 1 means no association.

What is NNH?

Number Needed to Harm: when exposure increases risk (RR > 1), NNH = 1/ARR.

How do I interpret a 95% CI that includes 1?

If the 95% CI for RR includes 1, the association is not statistically significant at α=0.05.

By the Numbers

RR=1
No Association
RR>1
Harmful Exposure
RR<1
Protective Exposure
NNT
1/|ARR|

Disclaimer: This calculator provides accurate epidemiological computations for educational and research reference. For clinical decisions, consult qualified epidemiologists.

👈 START HERE
⬅️Jump in and explore the concept!
AI

Related Calculators

Odds Calculator

Convert between probability, odds (for/against), decimal odds, fractional odds, and American (moneyline) odds. Compute odds ratio for 2×2 contingency tables.

Statistics

Accuracy Calculator

Compute classification metrics from a confusion matrix: Accuracy, Precision, Recall, F1 Score, Specificity, MCC, and more. Essential for ML model evaluation.

Statistics

Bayes' Theorem Calculator

Calculate posterior probabilities using Bayes' theorem. Input prior, likelihood, and evidence to update beliefs with step-by-step Bayesian reasoning.

Statistics

Bertrand's Box Paradox

Interactive Bertrand's Box Paradox simulator. Explore why the probability of the other coin being gold is 2/3, not 1/2, with Monte Carlo simulation and Bayesian proof.

Statistics

Bertrand's Paradox

Explore Bertrand's Paradox — three valid methods for choosing a random chord give three different probabilities (1/3, 1/2, 1/4). Interactive simulation and visualization.

Statistics

Birthday Paradox Calculator

Calculate the probability that at least two people in a group share the same birthday. Interactive chart showing probability vs group size.

Statistics