# Turning Circle/Radius Calculator

How do you determine the turning radius of a vehicle? The **Turning Radius Calculator** helps you find out. The turning radius is the smallest circular turn a vehicle can make. This calculator can be used in two modes: Basic and Advanced.

### How to Use the Calculator

#### Basic Calculator

**Wheel Base (m)**: Enter the wheel base of the vehicle, such as`2.5`

meters.**Turn Angle (degrees)**: Input the turn angle, for instance,`30`

degrees.**Turning Radius (m)**: Leave this blank to calculate the turning radius, or input a value if you want to calculate the wheel base or turn angle.

#### Advanced Calculator

**Wheel Base (m)**: Enter the wheel base of the vehicle, for example,`2.8`

meters.**Turn Angle (degrees)**: Input the turn angle, such as`45`

degrees.**Track Width (m)**: Enter the track width, like`1.6`

meters.**Coefficient of Friction**: Input the coefficient of friction, for instance,`0.8`

.

### Formula

For the basic calculator, the formula to find the turning radius is:

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

**Variables**

Variable | Description |
---|---|

TR | Turning Radius (m) |

WB | Wheel Base (m) |

a | Turn Angle (degrees) |

### How To Calculate Car Turning Radius

#### Example 1: Basic Calculator

**Wheel Base (m)**: 3.0 meters**Turn Angle (degrees)**: 35 degrees**Turning Radius (m)**: Leave blank

To calculate the **Turning Radius**:

1. Convert the turn angle to radians:

$a=35\times \frac{\pi}{180}=0.6109\text{\hspace{0.17em}}\text{radians}$

2. Use the formula:

$\text{TR}=\frac{3.0}{\mathrm{tan}(0.6109)}$

3. Calculate:

$\text{TR}=\frac{3.0}{0.7002}=4.28\text{\hspace{0.17em}}\text{meters}$

So, the turning radius is **4.28 meters**.

#### Example 2: Advanced Calculator

**Wheel Base (m)**: 2.5 meters**Turn Angle (degrees)**: 40 degrees**Track Width (m)**: 1.5 meters**Coefficient of Friction**: 0.85

To calculate the **Optimal Speed for Turn**:

1. Convert the turn angle to radians:

$a=40\times \frac{\pi}{180}=0.6981\text{\hspace{0.17em}}\text{radians}$

2. Calculate the turning radius:

$\text{TR}=\frac{2.5}{\mathrm{sin}(0.6981)}$

$\text{TR}=\frac{2.5}{0.6428}=3.89\text{\hspace{0.17em}}\text{meters}$

3. Calculate the inside wheel turn radius:

$\text{Inside Wheel TR}=3.89-\frac{1.5}{2}=3.14\text{\hspace{0.17em}}\text{meters}$

4. Calculate the optimal speed:

$\text{Optimal Speed}=\sqrt{3.14\times 0.85\times 9.81}\times 3.6$

$\text{OptimalSpeed}=\sqrt{26.15}\times 3.6=5.11\times 3.6=18.38\text{\hspace{0.17em}}\text{km/h}$

So, the optimal speed for the turn is **18.38 km/h**.

Thank you for using our tool.