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

$v_{(km.h^{-1})} = \frac{3}{25}.\pi.r.N_{(rpm)}$

Where:

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

To convert rpm to km/h, you can use this online converter.

To convert rpm (revolutions per minute) to km/h (kilometers per hour), you need additional information about the system, specifically the radius or diameter of the wheel or rotating object. Here's a step-by-step process:

1. Determine the circumference of the wheel:

The circumference $C$ can be calculated using the radius $r$ expressed in meters:
$C = 2\pi r$

2. Calculate the distance traveled per minute:

Multiply the circumference $C$ by the rpm value to find the distance traveled per minute:

$\text{Distance per minute} = C \times \text{rpm}$

3. Convert the distance in kilometers:

$\text{Kilometers per minute} = \frac{C \times \text{rpm}}{1000}$

1. Convert the distance per minute to distance per hour:

Multiply the distance traveled per minute by 60 to convert it to kilometers per hour (km/h):

$\text{Speed in km/h} = \frac{60 \times C \times \text{rpm}}{1000} = \frac{3}{25} \times \pi \times r \times \text{rpm}$

### Example Calculation

Suppose you have a wheel with a diameter of 0.5 meters (which is 0.0005 kilometers), and it rotates at 3000 rpm.

1. Calculate the circumference:

$C = \pi d = \pi \times 0.0005 \, \text{km} \approx 0.00157 \, \text{km}$

1. Distance traveled per minute:

$\text{Distance per minute} = 0.00157 \, \text{km} \times 3000 = 4.71 \, \text{km}$

1. Convert to km/h:

$\text{Speed in km/h} = 4.71 \, \text{km} \times 60 = 282.6 \, \text{km/h}$

So, at 3000 rpm, with a wheel diameter of 0.5 meters, the speed is approximately 282.6 km/h.

### General Formula

The general formula to convert rpm to km/h is:

$\text{Speed in km/h} = \pi d \times \text{rpm} \times 60$

where $d$ is the diameter of the wheel in kilometers.