# Lorentz Transformation of Velocity Calculator

The Lorentz Transformation of Velocity Calculator will calculate the:

1. 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: 🖹 Normal View🗖 Full Page View Calculator Precision (Decimal Places)0123456789101112131415 x-component of object's velocity in the system S connected to the Earth (vx) m/s y-component of object's velocity in the system S connected to the Earth (vy) m/s z-component of object's velocity in the system S connected to the Earth (vz) m/s Velocity of system S' relative to the system S at rest in the x-direction (Vx) m/s Velocity of system S' relative to the system S at rest in the y-direction (Vy) m/s Velocity of system S' relative to the system S at rest in the z-direction (Vz) m/s Speed of light in vacuum (c) m/s ∞ Real Number Results∑ Scientific Number Results c [speed of light in a vacuum] = m/s [metre per second]

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

x-component of object's velocity in the system S' moving at velocity V relative to the system S v'x calculation The x-component of object's velocity in the system S' moving at velocity V relative to the system S v'x is 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'y is 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'z is m/s [metre per second] vx' = vx - √Vx2 + Vy2 + Vz2/1 - √Vx2 + Vy2 + Vz2 ∙ vx/c2vx' = - √ 2 + 2 + 2/1 - √ 2 + 2 + 2 ∙ / 2vx' = - √ + + /1 - √ + + ∙ /vx' = - √/1 - √ ∙ /vx' = - /1 - ∙ /vx' = /1 - /vx' = /1 - vx' = /vx' = vy' = vy ∙ √1 - Vx2 + Vy2 + Vz2/c2/1 - √Vx2 + Vy2 + Vz2 ∙ vx/c2vy' = ∙ √1 - 2 + 2 + 2/ 2/1 - √ 2 + 2 + 2 ∙ / 2vy' = ∙ √1 - + + //1 - √ + + ∙ /vy' = ∙ √1 - //1 - √ ∙ /vy' = ∙ √1 - /1 - ∙ /vy' = ∙ √/1 - /vy' = ∙ /1 - vy' = /vy' = vz' = vz ∙ √1 - Vx2 + Vy2 + Vz2/c2/1 - √Vx2 + Vy2 + Vz2 ∙ vx/c2vz' = ∙ √1 - 2 + 2 + 2/ 2/1 - √ 2 + 2 + 2 ∙ / 2vz' = ∙ √1 - + + //1 - √ + + ∙ /vz' = ∙ √1 - //1 - √ ∙ /vz' = ∙ √1 - /1 - ∙ /vz' = ∙ √/1 - /vz' = ∙ /1 - vz' = /vz' = x-component of object's velocity in the system S connected to the Earth (vx) m/s [metre per second] y-component of object's velocity in the system S connected to the Earth (vy) m/s [metre per second] z-component of object's velocity in the system S connected to the Earth (vz) m/s [metre per second] Velocity of system S' relative to the system S at rest in the x-direction (Vx) m/s [metre per second] Velocity of system S' relative to the system S at rest in the y-direction (Vy) m/s [metre per second] Velocity of system S' relative to the system S at rest in the z-direction (Vz) m/s [metre per second] Speed of light in vacuum (c) m/s [metre per second]

## Related Physics Sections with Tutorials

Section 3: Kinematics

Section 18: Relativity

Section 22: Cosmology

## x-component of object's velocity in the system S' moving at velocity V relative to the system S v'x Formula and Calculation

vx' = vx - √Vx2 + Vy2 + Vz2/1 - Vx2 + Vy2 + Vz2 ∙ vx/c2

## y-component of object's velocity in the system S' moving at velocity V relative to the system S v'y Formula and Calculation

vy' = vy ∙ √1 - Vx2 + Vy2 + Vz2/c2/1 - Vx2 + Vy2 + Vz2 ∙ vx/c2

## z-component of object's velocity in the system S' moving at velocity V relative to the system S v'z Formula and Calculation

vz' = vz ∙ √1 - Vx2 + Vy2 + Vz2/c2/1 - Vx2 + Vy2 + Vz2 ∙ vx/c2

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

|V | = √Vx2 + Vy2 + Vz2

where

## Relativity Physics Tutorials associated with the Lorentz Transformation Of Velocity Calculator

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.

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