What is the incidence rate?
Type the number of new cases and either the person-time at risk or the number of people at risk at the start. The incidence rate calculator gives the incidence rate or the incidence proportion (risk, attack rate), per 100 up to per 1,000,000.
- Incidence
- 2.5
The incidence is 2.5 new cases per 1,000 person-years.
- Without the multiplier
- 0.0025
- Unit
- new cases per 1,000 person-years
Incidence: 2.5. The incidence is 2.5 new cases per 1,000 person-years.
How to calculate
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.
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.
Method: Incidence rate = new cases ÷ person-time at risk × 10ⁿ; incidence proportion = new cases ÷ population at risk at the start × 10ⁿ.
- 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
Each example is checked against the calculator on every build.
- Measure Incidence rate, New cases 16, Person-time at risk 6,400, Show per per 1,000 gives Incidence 2.5, Without the multiplier 0.0025, Unit 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
- Measure Incidence proportion, New cases 16, People at risk at the start 2,100, Show per per 1,000 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
- Measure Incidence proportion, New cases 100, People at risk at the start 189, Show per per 100 (percent) 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
- Measure Incidence rate, New cases 72, Person-time at risk 1,862, Show per per 1,000 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
- Measure Incidence rate, New cases 44,232, Person-time at risk 290,809,777, Show per per 100,000 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
How it works
Pick one of two measures from CDC's Principles of Epidemiology, Lesson 3:
- Incidence rate (person-time rate) = new cases during the period ÷ person-time at risk, × 10ⁿ. Person-time is the time each person was observed while at risk, added up for everyone, in years, months or days. The unit only names the result ("per 1,000 person-years"); the page does not convert it.
- Incidence proportion (risk, attack rate) = new cases during the period ÷ people at risk at the start of the period, × 10ⁿ.
The multiplier 10ⁿ is one of 1, 100 (a percent), 1,000, 10,000, 100,000 or 1,000,000. The page also shows the value without the multiplier (cases per person-time unit, or per person).
Unit text. The page names the result in words. A rate reads new cases per 1,000 person-years (or person-months, person-days; years when no unit is chosen), and a proportion reads new cases per 1,000 people at risk. The multiplier is written with thousands commas: per 100, per 10,000, per 1,000,000. With the multiplier 1 the words are singular: new cases per person-year (or person-month, person-day) and new cases per person at risk.
Rules. New cases is a whole number, 0 or more. Person-time is at least 0.000001. People at risk is a whole number, 1 or more, and for the incidence proportion the new cases cannot be more than the people at risk.
Rounding. The result is the exact quotient of the typed numbers, rounded once for display to 2 decimals (the value without the multiplier to 6 significant figures). So a result below 0.005 shows as 0: with the multiplier 1, 16 cases in 6,400 person-years shows 0 per person-year, and the value without the multiplier shows 0.0025. Choose a larger multiplier to read such a rate.
Worked examples by hand
Heart disease cohort (page default). 16 new cases, 6,400 person-years. 16 ÷ 6,400 = 0.0025 per person-year; × 1,000 = 2.50 per 1,000 person-years.
The same cohort as a proportion. 16 new cases among 2,100 women at the start. 16 ÷ 2,100 × 1,000 = 7.62 per 1,000 over the 4 years.
Diabetic men, as a percent. 100 deaths among 189 men. 100 ÷ 189 × 100 = 52.91%.
Diabetic women. 72 deaths in 1,862 person-years. 72 ÷ 1,862 × 1,000 = 38.668, shown as 38.67 per 1,000 person-years. CDC prints 38.6: it cuts the value at 1 decimal, where rounding gives 38.7.
AIDS in the United States, 2003. 44,232 new cases; mid-year population 290,809,777, used as one year of person-time. 44,232 ÷ 290,809,777 × 100,000 = 15.21 per 100,000.
Other questions people ask
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.