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The will calculate the:

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

**Calculation Parameters:** All relativistic events are supposed to occur in vacuum; all systems are inertial. All units are in metres, there is a handy "Speed of Light in a Vacuum to Metres Converter" under the calculator to allow conversion from speed of light to metres as required to complete your computations.

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-coordinate of object or event in the system S' moving at velocity V relative to the system S x' is m [metre] |

The y-coordinate of object or event in the system S' moving at velocity V relative to the system S y' is m [metre] |

The z-coordinate of object or event in the system S' moving at velocity V relative to the system S z' is m [metre] |

x-coordinate of object or event in the system S' moving at velocity V relative to the system S x' calculations |
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x' = x - V_{x} ∙ t/√1 - V^{2}_{x}/c^{2}x' = - ∙ /√1 - ^{2}/^{2}x' = /√1 - /x' = /√1 - x' = /√x' = /x' = |

y-coordinate of object or event in the system S' moving at velocity V relative to the system S y' calculations |

y' = y - V_{y} ∙ t/√1 - V^{2}_{y}/c^{2}y' = - ∙ /√1 - ^{2}/^{2}y' = /√1 - /y' = /√1 - y' = /√y' = /y' = |

z-coordinate of object or event in the system S' moving at velocity V relative to the system S z' calculations |

z' = z - V_{z} ∙ t/√1 - V^{2}_{z}/c^{2}z' = - ∙ /√1 - ^{2}/^{2}z' = /√1 - /z' = /√1 - z' = /√z' = /z' = |

Lorentz Transformation Of Coordinates Calculator Input Values |

x-coordinate of object or event in the system S connected to the Earth (x) m [metre] |

y-coordinate of object or event in the system S connected to the Earth (y) m [metre] |

z-coordinate of object or event in the system S connected to the Earth (z) m [metre] |

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] |

Time of event's occurrence in the system S connected to the Earth (t) s [second] |

Speed of light in vacuum (c) s [second] |

x' = *x - V*_{x} ∙ t*/**√***1 - ***V*^{2}_{x}*/**c*^{2}

y' = *y - V*_{y} ∙ t*/**√***1 - ***V*^{2}_{y}*/**c*^{2}

z' = *z - V*_{z} ∙ t*/**√***1 - ***V*^{2}_{z}*/**c*^{2}

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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