Incidence Rate & Cumulative Incidence Calculator
Compute person-time incidence rates (PY, PM, PD) or population-at-risk cumulative incidence with verified 95% confidence intervals.
Use the Incidence Rate & Cumulative Incidence Calculator
Study Parameters
Observed new incident events during the observation window.
Sum of individual disease-free observation periods.
Initial disease-free cohort size (N ≥ new cases).
Evidence Presets
Enter case and denominator parameters to view rate estimates, exact 95% confidence intervals, and reference scales.
Multi-Scale Comparison
| Scale | Estimate | 95% Confidence Interval |
|---|
Interpretation
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Epidemiological Unit Relationships
Incidence Rate (Incidence Density): Measures event frequency per unit of aggregate observation time. Standard reference ratios: 1 person-year is observationally equivalent to 12 person-months or ~365.25 person-days. Rates are rates of occurrence, not percentages; when follow-up time is short or risk is high, a rate can validly exceed 1.0.
Cumulative Incidence (Incidence Proportion / Risk): Measures probability of event occurrence in a fixed cohort initially at risk:
Risk = Cases ÷ N_initial. Because numerator is a subset of denominator, values are strictly bounded within [0, 1] (or 0% to 100%).
Statistical Interval Methods & Authorities
Garwood Poisson Limits: Exact limits for observed count k at confidence 100(1 - α)%:
Lower = χ²2k(α/2) / 2; Upper = χ²2k+2(1 - α/2) / 2.
When k = 0, the lower bound is exactly 0 and upper bound is -ln(α/2) = -ln(0.025) ≈ 3.688879.
Wilson Score Interval: Recommended for binomial proportions without ad-hoc continuity adjustments (NIST Handbook §2.4.1).
Primary authorities: CDC Principles of Epidemiology (Lesson 3.2) • CDC U.S. Cancer Statistics (Poisson CIs) • NIST e-Handbook §2.4.1.
Educational Limitation: This calculator provides statistical point and interval estimation for research, teaching, and surveillance analysis. It does not provide clinical diagnoses or individualized prognostic recommendations.
Summary
The Incidence Rate Calculator provides epidemiologists, public health practitioners, and researchers with exact calculations for both incidence density (rates per person-time at risk) and cumulative incidence (attack rate or proportion at risk). Results include exact two-sided 95% confidence intervals and multi-scale rate reference comparisons.
How it works
- Choose your epidemiological calculation mode: Person-Time Incidence Rate or Cumulative Incidence (Risk).
- Enter the observed count of new confirmed cases.
- Enter either the summed person-time at risk (with units) or the starting population at risk.
- Select your preferred reporting multiplier base (100, 1,000, 10,000, or 100,000).
- Review the point estimate, exact 95% confidence interval, mathematical formula, and multi-scale conversion table.
Use cases
- Cohort and longitudinal study morbidity reporting.
- Outbreak investigation attack rate and risk proportion assessment.
- Public health surveillance and vital statistics disease burden monitoring.
- Translating rates across surveillance denominators (1,000 vs 10,000 vs 100,000).
- Academic epidemiological teaching and biostatistical coursework.