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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.

Lorentz Transformation of Velocity Calculator
Handy Speed of Light in a Vacuum to Metres Converter:
=

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

Lorentz Transformation of Velocity Calculator Results (detailed calculations and formula below)
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]
x-component of object's velocity in the system S' moving at velocity V relative to the system S v'x calculation
vx' = vx - √Vx2 + Vy2 + Vz2/1 - √Vx2 + Vy2 + Vz2 ∙ vx/c2
vx' = - √ 2 + 2 + 2/1 - √ 2 + 2 + 2 ∙ / 2
vx' = - √ + + /1 - √ + + ∙ /
vx' = - √/1 - √ ∙ /
vx' = - /1 - ∙ /
vx' = /1 - /
vx' = /1 -
vx' = /
vx' =
y-component of object's velocity in the system S' moving at velocity V relative to the system S v'y calculation
vy' = vy ∙ √1 - Vx2 + Vy2 + Vz2/c2/1 - √Vx2 + Vy2 + Vz2 ∙ vx/c2
vy' = ∙ √1 - 2 + 2 + 2/ 2/1 - √ 2 + 2 + 2 ∙ / 2
vy' = ∙ √1 - + + //1 - √ + + ∙ /
vy' = ∙ √1 - //1 - √ ∙ /
vy' = ∙ √1 - /1 - ∙ /
vy' = ∙ √/1 - /
vy' = ∙ /1 -
vy' = /
vy' =
z-component of object's velocity in the system S' moving at velocity V relative to the system S v'z calculation
vz' = vz ∙ √1 - Vx2 + Vy2 + Vz2/c2/1 - √Vx2 + Vy2 + Vz2 ∙ vx/c2
vz' = ∙ √1 - 2 + 2 + 2/ 2/1 - √ 2 + 2 + 2 ∙ / 2
vz' = ∙ √1 - + + //1 - √ + + ∙ /
vz' = ∙ √1 - //1 - √ ∙ /
vz' = ∙ √1 - /1 - ∙ /
vz' = ∙ √/1 - /
vz' = ∙ /1 -
vz' = /
vz' =
Lorentz Transformation Of Velocity Calculator Input Values
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]
Discover Physics with free Physics Revision Notes and Physics Calculator: Lorentz Transformation Of Velocity. This image shows the properties and lorentz transformation of velocity formula for the Lorentz Transformation Of Velocity. 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

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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.

|V⃗ | = √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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