Calculate a rate per 100,000 people from the number of cases and the population size, or use per 1,000 or find expected cases from a known rate.
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Per 100,000 Population Formula
The calculator uses three inverse formulas. The reporting base is 100,000 by default; choose another base to match a known crude population rate.
Cases to rate:
Rate to expected cases:
Population from events and a positive crude rate: Population = Events × Reporting base ÷ Known rate.
- Cases: count of events, diagnoses, deaths, or incidents observed.
- Population: number of people at risk during the same period.
- Rate Denominator: the standardization base (100,000 by default, but 1,000, 10,000, or 1,000,000 are also common).
- Known Rate: a published rate already expressed per some denominator.
- Target Population: the population you want to apply the known rate to.
The Cases to rate mode divides events by population and scales the result up to a fixed reference base so you can compare groups of different sizes. The Rate to cases mode does the reverse: it converts a known rate back into an expected number of events for a population you choose.
Reference Tables
Use these tables to sanity check your output and to pick a denominator that matches how the rate will be reported.
| Denominator | Typical use | Example |
|---|---|---|
| per 1,000 | Birth rates, infant mortality | 12 births per 1,000 |
| per 10,000 | Population event reporting | 3.5 events per 10,000 people |
| per 100,000 | Cancer, homicide, suicide, COVID-19 | 14 deaths per 100,000 |
| per 1,000,000 | Rare disease incidence, environmental risk | 2 per 1,000,000 |
| Rate per 100,000 | Percent | 1 case per N people |
|---|---|---|
| 1 | 0.001% | 100,000 |
| 10 | 0.01% | 10,000 |
| 100 | 0.1% | 1,000 |
| 1,000 | 1% | 100 |
| 10,000 | 10% | 10 |
Examples and FAQ
Example 1: Cases to rate. A county of 245,000 people reports 37 cases of a disease in one year. Rate = (37 / 245,000) × 100,000 = 15.10 per 100,000.
Example 2: Rate to cases. The state rate is 24 per 100,000. You manage a town of 18,500 people. Expected cases = (24 / 100,000) × 18,500 = 4.44 cases.
Why scale to 100,000? Raw counts depend on population size. Reporting per 100,000 puts crude rates on the same numerical scale, but does not adjust for age or other differences. Do not reverse an age-adjusted rate to infer actual event counts.
Can I get a fractional case? Yes, in Rate to cases mode. The result is a statistical expectation, not a whole-person count. Round only at the very end if you need a discrete number.
What time period should I use? Match the event count and population definition to the period being reported. A five-year total divided by a population estimate is not an annual rate. This calculator does not convert person-time denominators such as patient-days into population denominators.
Does this work for incidence and prevalence? It can scale a crude incidence measure based on a population at risk or a prevalence proportion using the appropriate population and time definition. A true person-time incidence rate uses a different denominator. The displayed event-to-population percentage is a proportion only when events count distinct members of that population.
