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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)=325.π.r.N(rpm)v_{(km.h^{-1})} = \frac{3}{25}.\pi.r.N_{(rpm)}

Where:

  • vv is the linear velocity expressed in kilometers per hour (km/h)
  • NN is the angular velocity expressed in revolution per minute (rpm)
  • rr 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 CC can be calculated using the radius rr expressed in meters:
    C=2πrC = 2\pi r

  2. Calculate the distance traveled per minute:

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

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

  3. Convert the distance in kilometers:

Kilometers per minute=C×rpm1000\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):

Speed in km/h=60×C×rpm1000=325×π×r×rpm\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=πd=π×0.0005 km≈0.00157 kmC = \pi d = \pi \times 0.0005 \, \text{km} \approx 0.00157 \, \text{km}

  1. Distance traveled per minute:

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

  1. Convert to km/h:

Speed in km/h=4.71 km×60=282.6 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:

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

where dd is the diameter of the wheel in kilometers.