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Mortality Rate Calculator

For epidemiology: compute the crude mortality rate (per 1,000 or 100,000), the cause-specific mortality rate, the case-fatality rate (CFR), the infant mortality rate (IMR) and proportional mortality — with the definitions from the CDC's Principles of Epidemiology.

Educational tool, not medical advice. These are standard epidemiologic measures of mortality in populations. They do not predict any individual's outcome. Case definitions, study design and confounding determine whether a rate is meaningful — consult an epidemiologist or clinician for real investigations.

Worked example

Numbers computed by this tool's own engine (oracle-verified). Population figures are the CDC's United States 2003 examples; the plague and proportional-mortality rows are illustrative:

MeasureResult
Crude mortality rate832.13 deaths per 100,000 population (2,419,921 deaths / 290,809,777 people)
Cause-specific rate (accidents)37.23 per 100,000 population (108,256 accident deaths / 290,809,777 people)
Case-fatality rate (pneumonic plague example)83.33% of diagnosed cases (10 deaths / 12 cases)
Infant mortality rate6.85 per 1,000 live births (28,025 infant deaths / 4,089,950 live births)
Proportional mortality (one cause)3.85% of all deaths (1,588 / 41,300 deaths)

Crude and cause-specific examples use the CDC's US 2003 figures (2,419,921 deaths; 290,809,777 estimated population; 108,256 accident deaths). Infant figures: 28,025 infant deaths and 4,089,950 live births, 2003. All values recomputed here with independent Decimal arithmetic.

Formulas used (CDC Principles of Epidemiology, Lesson 3, Table 3.4)

Crude mortality rate = deaths / mid-interval population × 1,000 (or 100,000) — the mortality rate from all causes of death for a population.

Cause-specific mortality rate = deaths from that cause / mid-interval population × 100,000 — the numerator is deaths attributed to one specific cause; the denominator stays the whole population.

Case-fatality rate (death-to-case ratio) = deaths / diagnosed cases × 100 — the share of ill people who die; a measure of lethality, not of population mortality.

Infant mortality rate = deaths under age 1 / live births × 1,000 — note the denominator is live births, not the population; the CDC notes it is technically a ratio, not a rate.

Proportional mortality = deaths from one cause / deaths from all causes × 100 — shows the relative importance of a cause; it is NOT a measure of the risk of dying from that cause.

Mortality measures at a glance

MeasureNumeratorDenominator× multiplier
Crude mortality rateAll deaths in the intervalMid-interval population1,000 or 100,000
Cause-specific mortality rateDeaths from that causeMid-interval population100,000
Case-fatality rateDeaths from the diseaseDiagnosed cases of the disease100 (%)
Infant mortality rateDeaths under age 1Live births1,000
Proportional mortalityDeaths from one causeDeaths from all causes100 (%)

Summary of CDC Table 3.4, "Frequently Used Measures of Mortality".

Frequently asked questions

What is the mortality rate formula?

Mortality rate = deaths during a given time period / size of the population among which the deaths occurred x multiplier. The CDC (Principles of Epidemiology, Lesson 3, Table 3.4) gives the crude mortality rate as (total deaths / mid-interval population) x 1,000 or x 100,000. For example, 2,419,921 deaths in a population of 290,809,777 gives 832.13 deaths per 100,000 population.

What is the difference between mortality rate and case-fatality rate (CFR)?

Their denominators are different. The mortality rate divides deaths by the population, so it measures how often death occurs in the population. The case-fatality rate divides deaths by diagnosed cases of the disease (x 100), so it measures lethality among the ill. A disease can have a low mortality rate (few deaths in the population) but a high CFR (most people who get it die).

What is the difference between mortality rate and incidence rate?

Incidence counts NEW CASES per person-time at risk; mortality counts DEATHS per population. Incidence measures how fast a disease is occurring; mortality measures how often death occurs. See the Incidence Rate Calculator for the person-time rate, cumulative incidence and rate ratios.

What is the difference between crude, cause-specific and proportional mortality?

Crude mortality uses all deaths over the whole population (per 1,000 or 100,000). Cause-specific mortality narrows the numerator to deaths from one cause, still over the whole population (usually per 100,000). Proportional mortality divides deaths from one cause by deaths from ALL causes (x 100) — it shows the relative importance of a cause, not the risk of dying from it.

Should I report per 1,000 or per 100,000?

The CDC uses both 1,000 and 100,000 for most mortality measures; cause-specific rates are usually reported per 100,000. The multiplier only rescales the number for readability — 8.32 per 1,000 = 832 per 100,000. State the multiplier you used so readers can compare.

Can the case-fatality rate be over 100%?

No — a CFR above 100% is impossible and signals a data problem: more deaths than diagnosed cases. Usually the deaths were counted from a larger or different group than the cases (for example, deaths that include earlier outbreaks divided by this week's cases). This calculator rejects deaths > cases and asks you to check the inputs.

What is the infant mortality rate and why is the denominator live births?

The infant mortality rate = deaths among children under age 1 / number of live births x 1,000, usually per year. The CDC notes it is technically a ratio rather than a rate, because some of the deaths in the numerator occurred among children born the previous year, who are not in the denominator. It is widely used to compare health status between populations.

Can I compare crude mortality rates between countries?

Only with caution. Crude rates reflect the population's age structure: a country with an older population will have a higher crude mortality rate even with the same health conditions. The CDC illustrates this with Alaska vs Florida — use age-specific or age-adjusted rates for fair comparisons.

What is the mortality rate of pneumonic plague?

Strictly speaking this is a case-fatality rate: among diagnosed cases, what share died. For example, 10 deaths among 12 diagnosed pneumonic plague cases gives a CFR of 10 / 12 x 100 = 83.33%. The WHO notes pneumonic plague is almost always fatal when left untreated, while bubonic plague has a CFR of 30% to 60% untreated — antibiotics are effective when given early. These figures describe lethality among the ill, not the death rate in the general population.

Is this tool medical advice?

No. It is an educational calculator for standard epidemiologic measures of mortality in populations, using the definitions from the CDC's Principles of Epidemiology. It does not diagnose, predict any individual's outcome, or replace professional epidemiologic analysis.

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Educational tool, not medical advice. Mortality measures describe populations, not individuals. They do not diagnose, predict anyone's outcome, or replace professional epidemiologic analysis.

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