Traffic Flow Calculator Formula

Understand the math behind the traffic flow calculator. Each variable explained with a worked example.

Formulas Used

Traffic Flow Rate (q)

flow = density * speed

Average Time Headway

headway = 3600 / (density * speed)

Average Spacing

spacing = 1000 / density

Variables

VariableDescriptionDefault
densityVehicle Density (k)(veh/km)30
speedSpace Mean Speed (u)(km/h)60

How It Works

Fundamental Traffic Flow Equation

Traffic flow, density, and speed are linked by a fundamental relationship.

Formula

q = k u

where q is flow rate (vehicles/hour), k is density (vehicles/km), and u is space mean speed (km/h).

Time headway = 3600/q seconds. Spacing = 1000/k metres. At capacity, flow is maximised with moderate speed and density.

Worked Example

30 vehicles per km travelling at 60 km/h.

density = 30speed = 60
  1. 01q = 30 x 60 = 1800 vehicles/hour
  2. 02Headway = 3600 / 1800 = 2.0 seconds
  3. 03Spacing = 1000 / 30 = 33.3 m between vehicles

Frequently Asked Questions

What is the capacity of a highway lane?

A typical freeway lane can carry 2000-2400 vehicles per hour at capacity. This occurs at moderate speeds (50-70 km/h) and medium density. Adding more vehicles beyond capacity causes flow breakdown and congestion.

What is the difference between flow and volume?

Volume is the total vehicles counted over a period (e.g., daily volume). Flow rate is the equivalent hourly rate during a specific interval (often 15-minute peak). Peak flow can be much higher than average hourly volume.

What happens when density gets too high?

As density increases beyond the critical value, speed drops sharply and flow actually decreases (the congested regime). This is the backward-bending portion of the speed-flow curve that characterises traffic jams.

Ready to run the numbers?

Open Traffic Flow Calculator