U.S. Department of Transportation
Federal Highway Administration
1200 New Jersey Avenue, SE
Washington, DC 20590
202-366-4000


Skip to content
FacebookYouTubeTwitterFlickrLinkedIn

Safety

eSubscribe
eSubscribe Envelope

FHWA Home / Safety / Transportation Safety Planning (TSP) / Transportation Safety Planning (TSP)

Transportation Safety Planning (TSP)

Graphical header that has the title: Applying Safety Data and Analysis to Performance-Based Transportation Planning.

Appendix C. Risk Ratio

The risk ratio compares the severity of crashes associated with a particular factor to the severity of all other crashes (e.g., the percentage of angle crashes that result in a serious injury or fatality divided by the percentage among all other crashes, excluding angle crashes). Crash types or factors with a risk ratio greater than 1 are overrepresented with respect to severe crashes. Formally, the risk ratio is defined by the following equation.

Figure C.1 Equation. Risk Ratio

Equation: The risk ratio is calculated by dividing A by A+B, and then dividing that quotient by C divided by C+D.

Where:

A = the number of severe crashes of a particular type or emphasis area;

B = the total number of nonsevere crashes of the same type as in A;

C = the number of severe crashes, excluding those of the same type as in A; and

D = the total number of nonsevere crashes, excluding those of the same type as in A.

To illustrate this concept further, a few examples are provided below. Conventionally, data used to compute the risk ratio (variables A, B, C, and D) are arranged in a 2×2 matrix, where the first row corresponds to the numerator values in the formula above, and the second row corresponds to the denominator values.

Table C.1 Risk Ratio Data for Crashes in Rural Areas
Empty cell Severe Crash Not a Severe Crash Total Crashes
Rural Area 523 (A) 5,768 (B) 6,291 (A+B)
Not a Rural Area (Urban Area) 700 (C) 24,396 (D) 25,096 (C+D)

Source: Sample data, Cambridge Systematics, Inc., 2015.

Given this data, the formula to calculate the risk ratio is as follows:

Figure C.2 Equation. Severe Crash Risk Ratio for Rural Areas

Equation: 523 severe rural crashes are divided by 6,291 total rural crashes. The quotient is divided by 700 urban severe crashes divided by 25,096 total urban crashes. The result is 3.0.

Based on this calculation, crashes in rural areas are around three times more likely to result in a fatality or serious injury than those in urban areas.

A similar example for DUI crashes is provided here:

Table C.2 Risk Ratio Data for DUI Crashes
Empty cell Severe Crash Not a Severe Crash Total Crashes
DUI 201 (A) 1,589 (B) 1,790 (A+B)
Not a DUI 1,022 (C) 28,575 (D) 29,597 (C+D)

Source: Sample data, Cambridge Systematics, Inc., 2015.

Figure C.3 Equation. Severe Crash Risk Ratio for DUI Crashes

Equation: 201 severe driving under the influence crashes are divided by 1,790 total driving under the influence crashes. The quotient is divided by 1,022 non-driving under the influence crashes divided by 29,597 driving under the influence crashes. The result is 3.25. Meaning, driving under the influence areas are slightly more than three times more likely to result in a fatality or serious injury than nondriving under the influence crashes.

A risk ratio can also be developed for a combination of factors. An example for DUI crashes in rural areas is shown here:

Table C.3 Risk Ratio Data for Rural DUI Crashes
Empty cell Severe Crash Not a Severe Crash Total Crashes
Rural DUI Crash 93 (A) 597 (B) 690 (A+B)
Not a Rural DUI Crash 1,130 (C) 29,567 (D) 30,697 (C+D)

Source: Sample data, Cambridge Systematics, Inc., 2015.

Figure C.4 Equation. Severe Crash Risk Ratio for DUI Crashes in Rural Areas

Equation: 93 severe rural, driving under the influence crashes are divided by 690 total rural, driving under the influence crashes. The quotient is divided by 1,130 nonrural, driving under the influence crashes divided by 30,697 total nonrural, driving under the influence crashes. The result is 3.7. Meaning, rural driving under the influence areas are approximately three times more likely to result in a fatality or serious injury than those in nonrural, driving under the influence crashes.

As an outcome of this step, the transportation planner would understand the categories of crashes by type, severity, contributing factor, or geography that may be a focus for planning and programming or that should be a consideration in nonsafety-specific projects.

<< Appendix B       Appendix D >>

Page last modified on December 11, 2015
Safe Roads for a Safer Future - Investment in roadway safety saves lives
Federal Highway Administration | 1200 New Jersey Avenue, SE | Washington, DC 20590 | 202-366-4000