The KM to RPM Calculator helps convert speed in kilometers per hour (KM/h) to revolutions per minute (RPM) for a wheel. This calculation is useful in various automotive and mechanical applications to understand the rotational speed of wheels or other rotating objects.

## Inputs

**Speed (S)**: The speed of the vehicle or object in kilometers per hour (KM/h).**Wheel Diameter (D)**: The diameter of the wheel in meters (m).

## Formulas and Calculations

## 1. Convert Speed to Meters per Minute

First, convert the speed from kilometers per hour to meters per minute:

[ S_{m/min} = S \times \frac{1000}{60} ]

where:

- ( S_{m/min} ) = Speed in meters per minute
- ( S ) = Speed in kilometers per hour

## 2. Calculate Wheel Circumference

Calculate the circumference of the wheel:

[ C = \pi \times D ]

where:

- ( C ) = Circumference of the wheel in meters
- ( D ) = Diameter of the wheel in meters

## 3. Convert Speed to Revolutions per Minute (RPM)

To find the RPM, divide the speed in meters per minute by the circumference of the wheel:

[ \text{RPM} = \frac{S_{m/min}}{C} ]

where:

- ( \text{RPM} ) = Revolutions per minute
- ( S_{m/min} ) = Speed in meters per minute
- ( C ) = Circumference of the wheel in meters

## Example Calculation

**Inputs:**

- Speed (S): 60 KM/h
- Wheel Diameter (D): 0.6 meters

**Convert Speed to Meters per Minute:**

[ S_{m/min} = 60 \times \frac{1000}{60} = 1000 \text{ m/min} ]

**Calculate Wheel Circumference:**

[ C = \pi \times 0.6 = 3.1416 \times 0.6 \approx 1.884 \text{ meters} ]

**Convert Speed to RPM:**

[ \text{RPM} = \frac{1000}{1.884} \approx 530.97 ]

## Summary

For a vehicle traveling at 60 KM/h with a wheel diameter of 0.6 meters, the wheel's rotational speed is approximately 530.97 RPM.

## Relevant Information Table

Speed (KM/h) | Wheel Diameter (m) | RPM |
---|---|---|

60 | 0.6 | 530.97 |

80 | 0.5 | 849.78 |

100 | 0.7 | 758.17 |

## Conclusion

The KM to RPM Calculator is a useful tool for anyone needing to convert speed in KM/h to RPM. It provides a quick and easy way to understand the rotational speed of wheels or machinery components based on their speed and size. This knowledge is vital in optimizing performance and ensuring the smooth operation of various mechanical systems.