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Open CalculatorAll Civil: Transportation PE Equations (25)
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All-Red Clearance Interval
Time for vehicle to clear intersection.
basic -
Average Daily Traffic (ADT)
Calculate ADT from directional design hour volume.
basicHigh Frequency -
Crash Rate (Intersections)
Crashes per million entering vehicles.
basic -
Crash Rate (Road Segments)
Crashes per 100 million vehicle-miles traveled.
basic -
Crest Vertical Curve Length (SSD)
Minimum crest curve length based on stopping sight distance.
intermediateHigh Frequency -
Elevation Difference (Direct)
Direct calculation of elevation difference between two points
basicHigh Frequency -
Equivalent Single Axle Load (ESAL)
Convert axle load to equivalent 18-kip single axle loads.
basicHigh Frequency -
Height of Instrument (HI)
Calculate the elevation of the instrument's line of sight
basicHigh Frequency -
Horizontal Curve - Long Chord
Straight-line distance from PC to PT.
basicHigh Frequency -
Horizontal Curve - External Distance
Distance from PI to midpoint of curve.
basicHigh Frequency -
Horizontal Curve - Curve Length
Arc length from PC to PT.
basicHigh Frequency -
Horizontal Curve - Middle Ordinate
Distance from midpoint of curve to midpoint of long chord.
basic -
Horizontal Curve - Radius from Degree
Calculate radius from degree of curve (arc definition).
basicHigh Frequency -
Horizontal Curve - Tangent Length
Distance from PC to PI (or PI to PT).
basicHigh Frequency -
Leveling Closure Error
Check for mathematical errors in differential leveling
basic -
Peak Hour Factor (PHF)
Ratio of hourly volume to peak flow rate within the hour.
basicHigh Frequency -
Pedestrian Crossing Time
Minimum pedestrian walk + clearance interval.
basic -
Sag Vertical Curve Length (Headlight)
Minimum sag curve length based on headlight sight distance.
intermediateHigh Frequency -
Stopping Sight Distance (SSD)
Distance needed to perceive, react, and brake to a stop.
intermediateHigh Frequency -
Minimum Radius (Superelevation)
Minimum curve radius for given speed, superelevation, and friction.
intermediateHigh Frequency -
Traffic Flow - Fundamental Equation
Relationship between flow, density, and speed.
basicHigh Frequency -
Turning Point Elevation
Calculate elevation of a turning point or foresight location
basicHigh Frequency -
Vertical Curve - Elevation at Station
Elevation at any point on a parabolic vertical curve.
intermediateHigh Frequency -
Vertical Curve - K Value
Rate of vertical curvature (horizontal distance per 1% grade change).
basicHigh Frequency -
Yellow Clearance Interval
Minimum yellow signal time based on ITE formula.
intermediateHigh Frequency
Frequently Asked Questions
How do I use All-Red Clearance Interval on the PE exam?
All-red clearance is typically 1-4 seconds for most intersections. Use conservative vehicle length (20-25 ft for mixed traffic). Approach speed should be 85th percentile or design speed, not speed limit. Often combined with yellow change interval for total clearance time.
How do I use Average Daily Traffic (ADT) on the PE exam?
Remember that K-factor represents the proportion of daily traffic occurring in the design hour, typically 0.08-0.15. Directional factor D is the proportion of design hour traffic in the peak direction, usually 0.55-0.70. These are given or must be estimated from facility type.
How do I use Crash Rate (Intersections) on the PE exam?
Always verify that ADT represents TOTAL entering vehicles from all approaches, not just one leg. The 1,000,000 factor standardizes to MEV (Million Entering Vehicles). Typical urban intersection rates: 0.3-1.5 crashes/MEV.
How do I use Crash Rate (Road Segments) on the PE exam?
Always verify units are consistent - if length is in km, result is crashes/100M veh-km. Common on PE exams in safety questions. Watch for trap answers that forget the 100 million factor. Study period should be at least 3 years for statistical validity.
How do I use Crest Vertical Curve Length (SSD) on the PE exam?
CRITICAL: This formula assumes S < L (sight distance less than curve length). If S > L, use the alternative formula L = 2S - 2158/A. Always check which case applies first. Constants are different for SI (658) vs English (2158) units.