user
What is the formula to convert kilometers per hour [km/h] to revolutions per minute [rpm] ?
alphonsio

The formula to convert a linear velocity expressed in kilometres per hour [km/h] to an angular velocity expressed in revolutions per minute [rpm] is given by:

$N_{(rpm)} = \frac{25}{3 \times \pi \times r} v_{(km/h)}$

Where:

• $v$ is the linear velocity expressed in kilometres per hour (km/h)
• $N$ is the angular velocity expressed in revolution per minute (rpm)
• $r$ is the radius expressed in meters (m)

Here is an online converter from km/h to rpm.

To convert speed from kilometers per hour (km/h) to revolutions per minute (rpm), you need to know the circumference of the wheel or rotating object that the speed is associated with. Here's a step-by-step guide to perform the conversion:

1. Determine the Wheel Circumference:

• The circumference $C$ of the wheel can be calculated using the formula:
$C = \pi \times d$
where $d$ is the diameter of the wheel.
2. Convert km/h to meters per minute (m/min):

• Since 1 kilometer = 1000 meters and 1 hour = 60 minutes, the conversion from km/h to m/min is:
$\text{Speed (m/min)} = \text{Speed (km/h)} \times \frac{1000}{60}$
3. Calculate the Revolutions per Minute (rpm):

• Once you have the speed in meters per minute and the circumference in meters, you can calculate the rpm:
$\text{RPM} = \frac{\text{Speed (m/min)}}{\text{Circumference (m)}}$

### Example Calculation

Suppose you have a vehicle moving at 60 km/h with a wheel diameter of 0.7 meters. Let's convert this speed to rpm.

1. Calculate the wheel circumference:

$C = \pi \times 0.7 \approx 3.14 \times 0.7 \approx 2.198 \text{ meters}$

2. Convert 60 km/h to meters per minute:

$\text{Speed (m/min)} = 60 \times \frac{1000}{60} = 1000 \text{ m/min}$

3. Calculate the RPM:

$\text{RPM} = \frac{1000}{2.198} \approx 455.87$

So, at 60 km/h, the wheels would be rotating at approximately 456 rpm.

### General Formula

If you want a general formula:

1. Convert km/h to m/min:
$\text{Speed (m/min)} = \text{Speed (km/h)} \times 16.6667$

2. Use the formula for RPM:

$\text{RPM} = \frac{\text{Speed (km/h)} \times 16.6667}{\pi \times \text{Wheel Diameter (m)}}$

This formula can be used for any given speed and wheel diameter.