INTRODUCTION TO SAFETY PERFORMANCE FUNCTIONS

Definition A safety performance function (SPF) is an equation used to predict the 

average number of crashes per year at a location as a function of exposure and, 

in some cases, roadway or intersection characteristics (e.g., number of lanes, traffic 

control, or median type) (1). For highway segments, exposure is represented by 

the segment length and annual average daily traffic (AADT) associated with the 

study section as shown by the sample SPF in Equation 1.

Predicted Crashes = exp[a + β * ln(AADT) + ln(Segment Length)] {1}

For intersections, exposure is represented by the AADT on the major and minor 

intersecting roads as shown by the sample SPF in Equation 2.

Predicted Crashes = exp[a + β1 * ln(AADTmajor) + β2 * ln(AADTminor)] {2}

Example 1: The SPF from the Highway Safety Manual (1) for total multiplevehicle (MV) crashes at urban, four-legged signalized intersections 

using Equation 2 where α, β1 and β2 were calculated separately is:

Predicted MV crashes = exp[-10.99 + 1.07*ln(AADTmajor) + 0.23*ln(AADTminor)]

For an urban, four-legged signalized intersection with a major road traffic 

volume (AADTmajor) of 25,000 vehicles per day and a minor road traffic 

volume (AADTminor) of 10,000 vehicles per day, the predicted number of MV 

crashes is computed as follows for the given SPF.

Predicted MV crashes = exp[-10.99 + 1.07*ln(25,000) + 0.23*ln(10,000)] = 

7.13 crashes/year

Application SPFs are used to predict crash frequency for a given set of 

site conditions. The predicted crashes from the SPF can be used alone 

or in combination with the site-specific crash history (i.e., Empirical 

Bayes method) to compare the safety performance of a specific 

site under various conditions. The Empirical Bayes method is used to 

estimate the expected long-term crash experience, which is a 

weighted average of the observed crashes at the site of interest and 

the predicted crashes from an SPF (2). 

The predicted number of crashes calculated using SPFs is 

instrumental for a number of activities in the project development 

process, including: 1) network screening, 2) countermeasure 

comparison, and 3) project evaluation.

1) Network Screening

SPFs can be used in the network screening process to determine 

whether the observed safety performance at a given location is 

higher or lower than the average safety performance of other 

sites with similar roadway characteristics and exposure. This is 

useful in the safety management process to identify sites with 

potential for safety improvement.

2) Countermeasure Comparison

SPFs can be used to predict the baseline crash frequency 

for given site conditions when comparing potential 

countermeasures. SPFs are used alone or in conjunction with 

the crash history to estimate the long-term crash frequency 

for baseline conditions (without treatment) and crash 

References

1. American Association of 

State Highway and 

Transportation Officials 

(AASHTO). Highway Safety 

Manual, 1st Edition, 

Washington, DC, 2010.

2. Hauer, E. Observational 

before-after studies in road 

safety. Pergamon Press, 

Elsevier Science Ltd., Oxford, 

England, 1997.

3. Introduction to Crash 

Modification Factors. Federal 

Highway Administration. 

Available online at: 

http://safety.fhwa.dot.gov/

tools/crf/resources/cmfs/.

4. Van Schalkwyk, I., Wemple, E.A., 

and Neuman, T.R. Integrating 

the HSM into the Highway Project 

Development Process. Publication 

FHWA-SA-11-50, Federal Highway 

Administration, Washington, DC, 

2012. 

Federal Highway Administration, Office of Safety, 

1200 New Jersey Avenue SE, Washington, DC 20590
modification factors (CMFs) are applied to estimate the crashes with treatment as shown in Equation 3. This 

is useful in activities where there are multiple alternatives to address safety concerns and it is desirable to 

quantify and compare the potential benefits of each treatment. Readers can refer to the Introduction to Crash 

Modification Factors for more information on CMFs and how they are applied (3). 

Predicted Crashes WITH Treatment = CMF * Predicted Crashes WITHOUT Treatment {3}

Example 2: Estimate the change in predicted crashes for installing left-turn lanes on two of the approaches at

an urban, four-legged signalized intersection with a major road traffic volume (AADTmajor) of 25,000 vehicles per 

day and a minor road traffic volume (AADTminor) of 10,000 vehicles per day. The CMF for installing left-turn lanes on 

two approaches at an urban, four-legged signalized intersection is 0.81 (1). 

Predicted crashes WITH treatment = CMF * Predicted crashes WITHOUT treatment (from Example 1)

Predicted crashes WITH treatment = 0.81 * 7.13 crashes/year = 5.78 crashes/year

The change in predicted crashes is a reduction of 1.35 crashes per year (7.13 – 5.78 crashes per year).

3) Project Evaluation

It is important to evaluate the safety effectiveness of roadway improvements to provide input to future planning, 

policy and programming decisions. The current state-of-the-practice is to employ the Empirical Bayes method 

in an observational before-after study to develop CMFs. SPFs are a critical component of the Empirical Bayes 

method, which combines the crash history for a given site with the predicted crashes from an SPF. In particular, 

the SPF helps to account for changes in traffic volume over time.

Calibration SPFs are developed using data from specific locations at a specific period in time and represent 

the average conditions for a given facility type. As such, it may be necessary to adjust the SPF through calibration 

to better reflect your local conditions or a different study period. A calibration procedure is presented in the 

Highway Safety Manual to reflect local conditions or a different study period (1). It is also necessary to adjust 

the SPF when the conditions at the site of interest differ from the average conditions. The Highway Safety Manual

identifies the base conditions for each SPF and provides applicable adjustment factors (i.e., CMFs) (1). CMFs are 

applied using Equation 4.

Adjusted Predicted Crash Frequency = CMF * Base Predicted Crash Frequency {4}

Example 3: Consider a scenario where it is desirable to predict crashes for a rural, two-lane study section with 

a segment length (L) of 2.0 miles and an AADT of 2,500 vehicles per day. It is determined that the roadway of 

interest has 11-ft lanes, while the base condition for the applicable SPF in the Highway Safety Manual is for a 

roadway with 12-ft lanes. All other conditions are similar to the base conditions. In this case, it is necessary 

to adjust the predicted crash frequency to reflect the different base condition using Equation 4. From the 

Highway Safety Manual, the applicable CMF for 11-ft lanes is 1.05 (1). The SPF for total crashes on 

rural, two-lane roads is similar to Equation 1 where a and β were calculated separately and shown in the 

following equation (1).

Predicted total crashes = exp[-15.22 + 1.68*ln(AADT) + ln(L)]

Base predicted crash frequency = exp[-15.22 + 1.68*ln(2,500) + ln(2.0)] = 0.25 crashes/year

Adjusted predicted crash frequency = CMF * Base predicted crash frequency

Adjusted predicted crash frequency = 1.05 * 0.25 crashes per year = 0.26 crashes per year

Readers can refer to the Highway Safety Manual (1) and FHWA’s Integrating the HSM into the Highway Project 

Development Process (4) for additional information and examples. The Highway Safety Manual provides specific 

SPFs for various facility types and details regarding the calibration process.

FHWA-SA-13-016