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Turning Radius Calculator

Formula

To calculate the turning radius:

$TR = \frac{WB}{\tan(a)}$

Where:

$TR$ is the turning radius
$a$ is the angle of the turn
$WB$ is the wheelbase (distance between centers of the front and back wheels)

What is a Turning Radius?

A turning radius is the radius at which a car will rotate, or turn, given a certain wheelbase length and an angle of turn of the wheels. This formula assumes a perfect theoretical turning scenario. In real-world situations, this turning radius would vary depending on wheel tilt, friction, and many other factors.

Example Calculation 1

Let's assume the following values:

Wheelbase ( $WB$ ) = 2.5 meters
Angle of Turn ( $a$ ) = 30 degrees

Using the formula:

Step 1: Convert the angle from degrees to radians:

$a_{rad} = \deg2rad(30) \approx 0.5236 \text{ radians}$

Step 2: Calculate the turning radius:

$TR = \frac{2.5}{\tan(0.5236)} \approx 4.33 \text{ meters}$

The turning radius is approximately 4.33 meters.

Example Calculation 2

Let's assume the following values:

Wheelbase ( $WB$ ) = 3 meters
Angle of Turn ( $a$ ) = 45 degrees

Using the formula:

Step 1: Convert the angle from degrees to radians:

$a_{rad} = \deg2rad(45) \approx 0.7854 \text{ radians}$

Step 2: Calculate the turning radius:

$TR = \frac{3}{\tan(0.7854)} \approx 3 \text{ meters}$

The turning radius is approximately 3 meters.