Attachment A - Yellow and Red Interval Equations.pdf

1 
ATTACHMENT A 
Current City of Phoenix equations for calculating the yellow change and red clearance 
intervals:  
Yellow Change Calculation 
𝑌𝑌≥𝑡𝑡+
1.47𝑉𝑉
2𝑎𝑎+ 64.4𝑔𝑔
Where: 
𝑌𝑌 = minimum yellow change interval (in seconds) with a maximum of 5 seconds (if the 
calculation exceeds 5 seconds, any excess time from the calculation is added to the red 
clearance interval); 
𝑡𝑡 = perception-reaction time (in seconds); the time needed for an approaching driver to 
“perceive” the yellow indication and to “react” by braking to a stop or deciding to pass 
through the intersection. Default value of 1.0 second. 
V = intersection entry speed (mph); the approach speed limit is assumed. 
𝑎𝑎 = deceleration (ft/second2); the rate at which it is assumed a driver will slow down 
upon seeing the yellow signal. Default value of 10 ft/second2. 
𝑔𝑔 = grade of approach (downhill is negative grade) 
Red Clearance Calculation 
𝑅𝑅= ൤𝑊𝑊
1.47𝑉𝑉൨ 
Where: 
𝑅𝑅 = red clearance interval (seconds); 
V= intersection entry speed (mph); the approach speed limit is assumed. 
𝑊𝑊 = distance to traverse the intersection (width), stop line to far side no-conflict point 
along the vehicle path (ft.);

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Current 2020 ITE-recommended equations for calculating the yellow change and red 
clearance intervals: 
 
Yellow Change Calculation 
 
𝑌𝑌≥𝑡𝑡+ 1.47(𝑉𝑉85 −𝑉𝑉𝐸𝐸)
𝑎𝑎+ 32.2𝑔𝑔
+
1.47𝑉𝑉𝐸𝐸
2𝑎𝑎+ 64.4𝑔𝑔 
 
Where: 
𝑌𝑌 = minimum yellow change interval (in seconds); 
𝑡𝑡 = perception-reaction time (in seconds); the time needed for an approaching driver to 
“perceive” the yellow indication and to “react” by braking to a stop or deciding to 
pass through the intersection. Default value of 1.0 second. 
𝑉𝑉85 = 85th percentile approach speed (mph); the speed at which a “reasonable” driver is 
assumed to approach the intersection. 
𝑉𝑉𝐸𝐸 = intersection entry speed (mph); the speed at which a “reasonable” driver is 
assumed to cross the stop line of the intersection when they have been slowing 
down in preparation for making a left turn. 
𝑎𝑎 = deceleration (ft/second2); the rate at which it is assumed a driver will slow down 
upon seeing the yellow signal. Default value of 10 ft/second2. 
𝑔𝑔 = grade of approach (downhill is negative grade) 
 
Red Clearance Calculation 
 
𝑅𝑅= ൤𝑊𝑊+ 𝐿𝐿
1.47𝑉𝑉𝐸𝐸
൨−𝑡𝑡𝑠𝑠 
Where: 
𝑅𝑅 = red clearance interval (seconds); 
𝑊𝑊 = distance to traverse the intersection (width), stop line to far side no-conflict point 
along the vehicle path (ft.); 
𝐿𝐿 = length of vehicle (ft.); 20 ft is often used as the representative length for vehicles 
entering the intersection. 
𝑡𝑡𝑠𝑠 = conflicting vehicular movement start up delay (seconds); an optional parameter with 
an initial value set at 0.0 seconds, values may be used based on engineering 
judgment or as supported by an engineering study.