Traffic Flow Calculator
Calculate traffic flow rate, density, and speed using the fundamental traffic flow equation. Enter values for instant results with step-by-step formulas.
Formula
q = k x u | Capacity = uf x kj / 4
Where q is flow rate (veh/hr), k is density (veh/mi), u is speed (mph), uf is free-flow speed, and kj is jam density. The Greenshields model assumes a linear speed-density relationship and yields a parabolic flow-density curve with maximum capacity at half the jam density.
Worked Examples
Example 1: Freeway Segment Analysis
Problem: A 3-lane freeway carries 5,400 vehicles per hour at a mean speed of 58 mph. Free-flow speed is 70 mph and jam density is 240 veh/mi. Determine LOS and v/c ratio.
Solution: Flow per lane = 5400 / 3 = 1800 veh/hr/ln\nDensity k = q / u = 5400 / 58 = 93.1 veh/mi total = 31.0 veh/mi/ln\nCapacity = uf x kj / 4 = 70 x 240 / 4 = 4200 veh/hr per lane\nTotal capacity = 4200 x 3 = 12,600 veh/hr\nV/C ratio = 5400 / 12600 = 0.429\nLOS based on density of 31.0 pc/mi/ln = LOS D (26-35 range)
Result: Density: 31.0 veh/mi/ln | V/C: 0.429 | LOS D (Approaching unstable flow)
Example 2: Two-Lane Highway Capacity Check
Problem: A two-lane highway has a volume of 1,200 veh/hr with average speed of 48 mph. Free-flow speed is 55 mph, jam density is 200 veh/mi. Is this near capacity?
Solution: Density = 1200 / 48 = 25.0 veh/mi total = 12.5 veh/mi/ln\nCapacity = uf x kj / 4 = 55 x 200 / 4 = 2750 veh/hr total\nV/C ratio = 1200 / 2750 = 0.436\nDensity per lane = 12.5, which is LOS B (11-18 range)\nHeadway = 3600 / (1200/2) = 6.0 seconds
Result: Density: 12.5 veh/mi/ln | V/C: 0.436 | LOS B (Reasonably free flow) | 6.0s headway
Frequently Asked Questions
What is the fundamental traffic flow equation and what does it describe?
The fundamental traffic flow equation is q = k x u, where q is the flow rate (vehicles per hour), k is the density (vehicles per mile), and u is the space mean speed (miles per hour). This deceptively simple equation describes the macroscopic relationship between the three fundamental traffic stream variables. It forms the basis of all traffic flow theory and is used in highway capacity analysis, traffic simulation, and congestion management. The equation tells us that traffic flow is the product of how many vehicles occupy a stretch of road and how fast they are moving. Understanding this relationship is essential because increasing density beyond a critical point actually reduces flow, which is the fundamental mechanism of traffic congestion and breakdown.
What is the Greenshields traffic flow model and its assumptions?
The Greenshields model, proposed by Bruce Greenshields in 1935, was the first mathematical model relating speed and density in traffic streams. It assumes a linear relationship: u = uf x (1 - k/kj), where uf is the free-flow speed and kj is the jam density. This leads to a parabolic flow-density relationship with maximum flow (capacity) occurring at the critical density kc = kj/2 and capacity speed uc = uf/2. While simple, this model captures the fundamental behavior that speed decreases as density increases. Its main limitation is that it assumes the speed-density relationship is linear across all densities, which field data shows is not exactly true. Real traffic data typically shows that speed remains near free-flow until density reaches a threshold, then drops more rapidly. Despite this, Greenshields remains widely used for its mathematical simplicity and reasonable approximations.
What is the difference between flow rate and volume in traffic engineering?
Volume is the total number of vehicles passing a point during a specified time period, typically one hour, while flow rate is the equivalent hourly rate at which vehicles pass a point during a sub-hourly period, typically the peak 15 minutes. The relationship is: flow rate = volume / PHF, where PHF is the Peak Hour Factor. For example, if 3,600 vehicles pass in one hour but 1,080 pass during the busiest 15 minutes, the hourly volume is 3,600 veh/hr but the peak flow rate is 1,080 x 4 = 4,320 veh/hr. The PHF = 3,600/4,320 = 0.833. This distinction matters because capacity analysis uses peak flow rates, not hourly volumes, since congestion occurs during the peak period within the peak hour. A PHF of 1.0 means perfectly uniform flow, while values below 0.80 indicate highly peaked demand.
How does traffic density relate to congestion and what is jam density?
Traffic density is the number of vehicles occupying a given length of road at an instant in time, measured in vehicles per mile (or per kilometer). As density increases from zero, flow initially increases because more vehicles are present. However, beyond the critical density, vehicles begin interfering with each other, speeds drop, and flow actually decreases despite more vehicles being present. This is the mechanism of congestion. Jam density (kj) is the theoretical maximum density when traffic comes to a complete standstill, typically 180-250 vehicles per mile per lane depending on vehicle mix and spacing. At jam density, speed and flow are both zero. The critical density (kc) where maximum flow occurs is approximately half the jam density in the Greenshields model. Traffic management strategies like ramp metering aim to keep density below the critical value to prevent breakdown.
What is the concept of traffic wave theory and shock waves?
Traffic wave theory, developed by Lighthill, Whitham, and Richards (LWR theory), describes how disturbances propagate through traffic streams as waves. When a vehicle brakes, the deceleration propagates backward through the traffic stream as a shock wave. The speed of this shock wave is calculated as w = (q2 - q1) / (k2 - k1), where the subscripts represent conditions upstream and downstream of the wave. Backward-moving shock waves (negative speed) create the familiar stop-and-go pattern in congested traffic. A vehicle at the back of a queue may have to stop long after the original disturbance has cleared. Understanding shock waves is essential for designing ramp metering systems, variable speed limits, and incident management strategies. Shock waves can persist for hours after the initial cause has been resolved, which is why traffic jams seem to appear without any visible reason.
How is traffic flow data collected and what technologies are used?
Traffic flow data is collected using a variety of technologies, each with different capabilities and accuracy levels. Inductive loop detectors embedded in the pavement are the most established method, counting vehicles and measuring speed and occupancy. Video detection systems use cameras with image processing algorithms to count vehicles and classify them by type. Radar and microwave sensors can measure speed and count vehicles without being embedded in the pavement. Bluetooth and Wi-Fi sensors detect electronic devices in passing vehicles to estimate travel times and origin-destination patterns. Modern connected vehicle data from GPS-equipped vehicles provides speed and travel time information across entire road networks. Crowdsourced data from smartphone apps like Google Maps and Waze provides real-time speed information. Each method has tradeoffs in cost, accuracy, maintenance requirements, and the types of data collected.