# What is the incidence rate?

Computes the incidence rate (new cases ÷ person-time at risk) or the incidence proportion (new cases ÷ population at risk), per 100 to per 1,000,000.

- Page: https://www.acalculator.org/statistics/incidence-rate-calculator
- JSON spec: https://www.acalculator.org/statistics/incidence-rate-calculator.json
- Version: abc0ab55fd32

## Default answer

Example with the default inputs (Measure Incidence rate, New cases 16, Person-time at risk 6,400, Person-time unit Years, Show per per 1,000): The incidence is 2.5 new cases per 1,000 person-years.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| m | Measure | Incidence rate uses person-time; incidence proportion (risk, attack rate) uses the people at risk at the start. |
| cases | New cases | The number of new cases of the disease or injury during the period. |
| pt | Person-time at risk | The time each person was observed while at risk, added up for everyone, in the unit below. |
| u | Person-time unit | The unit the person-time is counted in; it names the result. |
| pop | People at risk at the start | The size of the population at risk at the start of the period. |
| per | Show per | The multiplier 10ⁿ, chosen so the result is easy to read. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| incidence | Incidence | New cases ÷ the denominator, times the multiplier you chose. |
| raw | Without the multiplier | New cases ÷ the denominator, per person-time unit or per person. |
| text | Unit | What the incidence counts: new cases per the multiplier and denominator. |

## Method

Incidence rate = new cases ÷ person-time at risk × 10ⁿ; incidence proportion = new cases ÷ population at risk at the start × 10ⁿ.

## Assumptions

- Person-time counts only the time each person was at risk (free of the disease and followed up).
- The person-time unit only names the result; the page does not convert between years, months and days.

## Worked examples

1. m = rate, cases = 16, pt = 6,400, per = 1000 gives incidence = 2.5, raw = 0.0025, text = new cases per 1,000 person-years. Source: CDC, Principles of Epidemiology, Lesson 3, section 2, incidence rate example (16 ÷ 6,400 = 2.5 per 1,000 person-years); https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section2.html.
2. m = proportion, cases = 16, pop = 2,100, per = 1000 gives incidence = 7.619048. Source: CDC, Principles of Epidemiology, Lesson 3, section 2 (incidence proportion 16 ÷ 2,100 = 7.6 per 1,000); https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section2.html.
3. m = proportion, cases = 100, pop = 189, per = 100 gives incidence = 52.910053. Source: CDC, Principles of Epidemiology, Lesson 3, section 2 (100 ÷ 189 × 100 = 52.9%); https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section2.html.
4. m = rate, cases = 72, pt = 1,862, per = 1000 gives incidence = 38.668099. Source: CDC, Principles of Epidemiology, Lesson 3, section 2 (72 deaths in 1,862 person-years, printed as 38.6 per 1,000 person-years; 72 ÷ 1,862 × 1,000 = 38.668); https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section2.html.
5. m = rate, cases = 44,232, pt = 290,809,777, per = 100000 gives incidence = 15.209943. Source: CDC, Principles of Epidemiology, Lesson 3, section 2 (44,232 ÷ 290,809,777 × 100,000 = 15.21 per 100,000); https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section2.html.

## FAQ

### How do I calculate an incidence rate?

Divide the number of new cases by the total person-time at risk, then multiply by 10ⁿ to make it readable. 16 new cases in 6,400 person-years is 16 ÷ 6,400 = 0.0025 per person-year, or 2.5 per 1,000 person-years.

### What is person-time?

The time each person was observed while at risk of the disease, added up for everyone. A person followed for 3 years adds 3 person-years; someone lost after 6 months adds 0.5. It lets people who were followed for different lengths of time be counted fairly.

### What is the difference between incidence rate and incidence proportion?

The incidence rate divides by person-time and has a time unit (per person-year). The incidence proportion, also called risk or attack rate, divides by the number of people at risk at the start and is a share of people over the period, often given as a percent.

### Which multiplier should I use?

Any power of 10 that makes the number easy to read. CDC uses percents for attack rates, per 1,000 person-years for cohort studies, and per 100,000 for national disease rates.

### How is incidence different from prevalence?

Incidence counts new cases during a period. Prevalence counts everyone who has the condition at a point or during a period, new and old cases alike.

### Can I use a mid-year population as the denominator?

Yes, for a yearly rate. CDC divides a year’s new cases by the mid-year population as an estimate of the person-years at risk: 44,232 new AIDS cases ÷ 290,809,777 × 100,000 = 15.21 per 100,000 in 2003.

## Sources

- Centers for Disease Control and Prevention. Principles of Epidemiology in Public Health Practice, 3rd ed., Lesson 3, Section 2: Morbidity Frequency Measures (incidence proportion, incidence rate, person-time), retrieved 2026-10-18. https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section2.html