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The Lorentz Transformation of Velocity Calculator will calculate the:

- Lorentz transformation of velocity in relativistic events when the components of velocity in the system S connected to the Earth and the relative velocity of two systems are given.

**Calculation Parameters:** All relativistic events are supposed to occur in vacuum; all systems are inertial.

Handy Speed of Light in a Vacuum to Metres Converter: |
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**If the motion occurs in 1 or 2 dimensions only, please insert the value 0 in the corresponding box of quantities representing the missing direction**

The x-component of object's velocity in the system S' moving at velocity V relative to the system S v is ^{'}_{x} m/s [metre per second] |

The y-component of object's velocity in the system S' moving at velocity V relative to the system S v is ^{'}_{y} m/s [metre per second] |

The z-component of object's velocity in the system S' moving at velocity V relative to the system S v is ^{'}_{z} m/s [metre per second] |

x-component of object's velocity in the system S' moving at velocity V relative to the system S v calculation^{'}_{x} |
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v_{x}' = v_{x} - √V_{x}^{2} + V_{y}^{2} + V_{z}^{2}/1 - √V ∙ v_{x}^{2} + V_{y}^{2} + V_{z}^{2}_{x}/c^{2}v _{x}' = - √ ^{2} + ^{2} + ^{2}/1 - √ ∙ ^{2} + ^{2} + ^{2}/ ^{2}v _{x}' = - √ + + /1 - √ ∙ + + /v _{x}' = - √/1 - √ ∙ /v _{x}' = - /1 - ∙ /v _{x}' = /1 - /v _{x}' = /1 - v _{x}' = /v _{x}' = |

y-component of object's velocity in the system S' moving at velocity V relative to the system S v calculation^{'}_{y} |

v_{y}' = v_{y} ∙ √1 - V_{x}^{2} + V_{y}^{2} + V_{z}^{2}/c^{2}/1 - √V ∙ v_{x}^{2} + V_{y}^{2} + V_{z}^{2}_{x}/c^{2}v _{y}' = ∙ √1 - ^{2} + ^{2} + ^{2}/ ^{2}/1 - √ ∙ ^{2} + ^{2} + ^{2}/ ^{2}v _{y}' = ∙ √1 - + + //1 - √ ∙ + + /v _{y}' = ∙ √1 - //1 - √ ∙ /v _{y}' = ∙ √1 - /1 - ∙ /v _{y}' = ∙ √/1 - /v _{y}' = ∙ /1 - v _{y}' = /v _{y}' = |

z-component of object's velocity in the system S' moving at velocity V relative to the system S v calculation^{'}_{z} |

v_{z}' = v_{z} ∙ √1 - V_{x}^{2} + V_{y}^{2} + V_{z}^{2}/c^{2}/1 - √V ∙ v_{x}^{2} + V_{y}^{2} + V_{z}^{2}_{x}/c^{2}v _{z}' = ∙ √1 - ^{2} + ^{2} + ^{2}/ ^{2}/1 - √ ∙ ^{2} + ^{2} + ^{2}/ ^{2}v _{z}' = ∙ √1 - + + //1 - √ ∙ + + /v _{z}' = ∙ √1 - //1 - √ ∙ /v _{z}' = ∙ √1 - /1 - ∙ /v _{z}' = ∙ √/1 - /v _{z}' = ∙ /1 - v _{z}' = /v _{z}' = |

Lorentz Transformation Of Velocity Calculator Input Values |

x-component of object's velocity in the system S connected to the Earth (v_{x}) m/s [metre per second] |

y-component of object's velocity in the system S connected to the Earth (v_{y}) m/s [metre per second] |

z-component of object's velocity in the system S connected to the Earth (v_{z}) m/s [metre per second] |

Velocity of system S' relative to the system S at rest in the x-direction (V_{x}) m/s [metre per second] |

Velocity of system S' relative to the system S at rest in the y-direction (V_{y}) m/s [metre per second] |

Velocity of system S' relative to the system S at rest in the z-direction (V_{z}) m/s [metre per second] |

Speed of light in vacuum (c) m/s [metre per second] |

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v_{x}' = *v*_{x} - √**V**_{x}^{2} + V_{y}^{2} + V_{z}^{2}*/**1 - **√***V**_{x}^{2} + V_{y}^{2} + V_{z}^{2} ∙ v_{x}*/**c*^{2}

v_{y}' = *v*_{y} ∙ √**1 - ***V*_{x}^{2} + V_{y}^{2} + V_{z}^{2}*/**c*^{2}*/**1 - **√***V**_{x}^{2} + V_{y}^{2} + V_{z}^{2} ∙ v_{x}*/**c*^{2}

v_{z}' = *v*_{z} ∙ √**1 - ***V*_{x}^{2} + V_{y}^{2} + V_{z}^{2}*/**c*^{2}*/**1 - **√***V**_{x}^{2} + V_{y}^{2} + V_{z}^{2} ∙ v_{x}*/**c*^{2}

is the module (magnitude) of velocity of the system S' relative to the inertial system S considered at rest.

|V*⃗* | = √**V**_{x}^{2} + V_{y}^{2} + V_{z}^{2}

where

The following Physics tutorials are provided within the Relativity section of our Free Physics Tutorials. Each Relativity tutorial includes detailed Relativity formula and example of how to calculate and resolve specific Relativity questions and problems. At the end of each Relativity tutorial you will find Relativity revision questions with a hidden answer that reveals when clicked. This allows you to learn about Relativity and test your knowledge of Physics by answering the test questions on Relativity.

- 18.1 - Relativity. Galilean Transformations. Einstein's Postulates and Newton's Laws
- 18.2 - Classical Principle of Relativity
- 18.3 - Space and Time in Einstein Theory of Relativity
- 18.4 - Relativistic Transformation of Velocity and the Relativistic Doppler Effect
- 18.5 - Lorentz Transformations
- 18.6 - Relativistic Dynamics. Mass, Impulse and Energy in Relativity

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