What Is Mortality Rate? Formula, Worked Example, and Interpretation

A mortality rate is the number of deaths in a defined population over a specified time interval, divided by the size of that population and scaled by a power of ten (usually per 1,000 or per 100,000). It is the basic measure of how often death occurs in epidemiology, and the part that most often goes wrong is the denominator, not the arithmetic. This guide gives the formula with every symbol explained, a fully worked example, a reading table for the main rate types, and copy-ready code for Excel, R and Python.

What is a mortality rate? Definition in one paragraph

The US Centers for Disease Control and Prevention (CDC) defines a mortality rate as “a measure of the frequency of occurrence of death in a defined population during a specified interval.” Three parts matter: a count of deaths (the numerator), a defined population at risk (the denominator), and a stated time period. A mortality rate with any of the three missing cannot be compared with anyone else’s.

Mortality rate formula

CDC’s Principles of Epidemiology gives the general form:

Mortality rate = (deaths occurring during a given time period ÷ size of the population among which the deaths occurred) × 10ⁿ

• Deaths (numerator): the number of deaths counted in the interval, for the population and cause you are studying.
• Population (denominator): the size of the population in which those deaths occurred. For a cause-specific rate, CDC states that the denominator remains the size of the population at the midpoint of the time period.
• 10ⁿ (multiplier): a power of ten that turns a tiny decimal into a readable number. CDC notes that in the United States 1,000 and 100,000 are both used for most types of mortality rates.

Worked example with the arithmetic shown

Illustrative example with invented numbers, not real data. A town has an estimated midyear population of 250,000. During the calendar year, 1,900 residents die from all causes.

1. Divide deaths by population: 1,900 ÷ 250,000 = 0.0076.
2. Multiply by 1,000: 0.0076 × 1,000 = 7.6 deaths per 1,000 population per year.
3. The same rate per 100,000: 0.0076 × 100,000 = 760 deaths per 100,000 population per year.

Both lines describe the same rate. Only the multiplier changed, so always state which one you used. Of the 1,900 deaths, suppose 190 were attributed to one cause. The cause-specific rate is 190 ÷ 250,000 × 100,000 = 76 per 100,000. If 1,100 of the deaths occurred among the 40,000 residents aged 65 and over, the age-specific rate for that group is 1,100 ÷ 40,000 × 100,000 = 2,750 per 100,000.

For a real-data check on the method, CDC’s lesson reports 108,256 US deaths attributed to accidents (unintentional injuries) in 2003, a cause-specific mortality rate of 37.2 per 100,000 population. Working backwards, that rate implies a population of roughly 291 million (108,256 ÷ 37.2 × 100,000), the same order of magnitude as the US population that year.

Interpretation: crude, cause-specific, age-specific and adjusted rates

A single number means little until you know which kind of rate it is. The definitions below are CDC’s.

Rate type	What it measures (CDC wording)	Read it as
Crude mortality rate	The mortality rate from all causes of death for a population	All deaths in one population; it is not adjusted for age
Cause-specific mortality rate	The mortality rate from a specified cause for a population	Deaths from one cause only; the numerator counts just deaths attributed to it
Age-specific mortality rate	A mortality rate limited to a particular age group	Death frequency within one age group only
Age-adjusted mortality rate	A mortality rate statistically modified to eliminate the effect of different age distributions in the different populations	The rate to use when comparing populations with different age structures
Infant mortality rate	A ratio expressing the number of deaths among children under 1 year of age, usually per 1,000 live births	Deaths in the first year relative to live births, not relative to the infant population

Mortality rate vs case fatality rate

The two are easily confused because both count deaths. A mortality rate divides deaths by the whole population, including people who never had the condition. The case fatality rate divides deaths by the number of people with the disease, so it describes how deadly the disease is once someone has it. The attack rate is a different measure again: it counts new cases, not deaths.

Assumptions and common mistakes

• Comparing crude rates across different age structures. A population with more older residents will show a higher crude rate even if its age-specific rates are identical. Use age-adjusted rates, or a ratio such as the standardized mortality ratio, for comparisons.
• Wrong or unstated denominator. CDC uses the population at the midpoint of the interval. Mixing a midyear population for one group with a start-of-year count for another makes the rates incomparable.
• Treating the infant mortality rate as a true rate. CDC defines it as a ratio of deaths among children under 1 year of age to live births, usually per 1,000, rather than to the midyear population of children under 1.
• Mixing up mortality with case fatality. See the comparison above: the denominators answer different questions.
• Ignoring follow-up time. When people enter and leave a study at different times, a simple population denominator misleads. Rates built on person-time handle this, and the result is then an incidence-style rate (see prevalence vs incidence).
• Dropping the multiplier or the period. “760” alone is uninterpretable; “760 per 100,000 per year” is not.

How to report a mortality rate (APA-style wording)

Name the rate type, give the count and the denominator, and state the multiplier and the period. Example wording using the illustrative numbers above:

The crude all-cause mortality rate was 760 per 100,000 population per year (1,900 deaths; estimated midyear population of 250,000). The age-specific rate for residents aged 65 and over was 2,750 per 100,000 per year.

If you compare groups, report the age-adjusted rate and say which standard population was used.

How to calculate a mortality rate in Excel, R or Python

Excel

With deaths in cell A2 and the midyear population in B2, per 100,000:

=A2/B2*100000

With the example values (1,900 and 250,000) this returns 760.

R

deaths <- 1900
population <- 250000
rate_per_100k <- deaths / population * 100000
rate_per_100k  # 760

Python

deaths = 1900
population = 250000
rate_per_100k = deaths / population * 100000
print(rate_per_100k)  # 760.0

To express the rate per 1,000 instead, replace 100000 with 1000 (result 7.6).

FAQ

What is mortality rate?

It is the number of deaths in a defined population during a specified time interval, divided by the population size and multiplied by 1,000, 100,000 or another power of ten. CDC defines it as a measure of the frequency of occurrence of death in a defined population during a specified interval.

What is the mortality rate formula?

Deaths in the period ÷ population among which the deaths occurred × 10ⁿ. For 1,900 deaths in a population of 250,000, the rate is 760 per 100,000.

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

CDC notes both are used in the United States. State the multiplier every time you report a rate.

Is mortality rate the same as death rate?

The terms are often used interchangeably, but a rate is only interpretable when you name its type (crude, cause-specific, age-specific or age-adjusted) and its multiplier and period.

Sources

• CDC, Principles of Epidemiology in Public Health Practice, Lesson 3, Section 3: Measures of Risk (archived), archive.cdc.gov, checked 2026-10-29.
• CDC, Epidemiology Glossary, cdc.gov, checked 2026-10-29.

The worked example uses invented numbers for illustration and is not drawn from any source.