# Traffic Density Calculator

Created by Bogna Szyk
Last updated: Jan 14, 2023

This traffic density calculator helps you analyze the traffic on any road. Thanks to this tool, you will be able to estimate the traffic flow and density, as well as find out the average travel speed. Additionally, you will also be able to estimate the average distance between two consecutive cars on the road.

Keep reading to learn how to calculate the traffic density and flow, or take a look at our MPG calculator!

## What is the traffic flow?

Traffic flow is defined as the number of vehicles that pass by a point in a given time period. We usually express this value as an hourly rate - for example, you can observe a flow of 500 vehicles per hour on a highway.

Traffic flow is usually measured by observing a road and noting the number of vehicles passing you. To convert this number into the hourly rate, you need to use the following equation:

$\mathrm{flow} = \frac{n}{t}$

where $n$ is the number of vehicles that passed by a point during the time frame $t$.

The flow is equal to zero in two cases - either when there is no traffic (no cars present on the road) or when all vehicles are stuck in a traffic jam and cannot move forward.

## Traffic density formula

Traffic density is a second fundamental characteristic of any road. It tells you how significant is the congestion of cars on the road. If the density reaches its maximum, the flow drops to zero, forming a traffic jam.

We calculate density as the number of vehicles $m$ that occupy a segment of a road of a length $L$. To calculate it, simply divide these two values:

$\mathrm{density} = \frac{m}{L}$

The reciprocal of the traffic density is the headway - the distance between the front tip of two vehicles driving one after another.

## How to calculate average travel speed

The two values above - flow and density - are directly linked to the average travel speed. These three are called the fundamental characteristics of a traffic flow, and the following formula links them.

$\mathrm{flow} = \mathrm{speed} × \mathrm{density}$

This fundamental equation gives you the most basic information about the traffic on any road.

To calculate the travel speed with this traffic density calculator, follow these steps:

1. Measure how many vehicles pass one point in a given time frame. We can assume that during two minutes, 20 cars passed you by. It means that the traffic flow is equal to
$\mathrm{flow} = \frac{20}{2} = 10\ \frac{\mathrm{veh}}{min} = 600 \ \frac{\mathrm{veh}}{h}$
1. Count how many vehicles occupy a segment of a road at once. Let's say that on a segment of length 200 m, you spotted two cars. The traffic density is equal to
$\mathrm{density} = \frac{2}{200} = 0.01\ \frac{\mathrm{veh}}{m} = 10\ \frac{\mathrm{veh}}{km}$
1. Now, you can calculate the headway between the cars as the reciprocal of the density:
$\mathrm{headway} = \frac{1}{10}km = 100 m$
1. The last thing to do is to use the fundamental equation to find the average travel speed:
$\mathrm{flow} = \mathrm{speed} × \mathrm{density} \\\mathrm{speed} = \frac{\mathrm{flow}}{\mathrm{density}} \\\mathrm{speed} = \frac{600}{10} = 60\frac{km}{h}$
1. The average travel speed on this road is 60 km/h.

Be sure to look at our gas calculator, too!

## FAQ

### How do I calculate traffic flow?

In order to compute traffic flow, you need to:

1. Decide on a time frame t. For instance, 5 minutes.
2. Count the vehicles that passed by a point during the time t.
3. Divide the number of vehicles from Step 2 by the time t from Step 1.

### How do I calculate traffic density?

In order to compute traffic density, you need to:

1. Choose a segment of a road and measure its length L.
2. Count the vehicles that occupy this segment.
3. Divide the number of vehicles from Step 2 by the length L from Step 1.

### What is the traffic flow if I saw 120 cars over 5 minutes?

The traffic flow is 0.4 cars/second or 1,440 cars/hour. To arrive at these numbers, divide the number of vehicles by the time, adjusting the time unit according to your needs. For instance, 5 minutes is 300 seconds, so the traffic flow is 120 / 300 = 0.4.

Bogna Szyk
Traffic flow
No. of vehicles
that pass during...
sec
Traffic flow
vehicles/
hr
Traffic density
No. of vehicles
mi
Density
vehicles/
mi
Average speed
ft
Travel speed
mph
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