Lorentz Transformation of Coordinates Calculator | iCalculator™

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.

Lorentz Transformation of Coordinates Calculator
Handy Speed of Light in a Vacuum to Metres Converter:
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Calculator Precision (Decimal Places)
x-coordinate of object or event in the system S connected to the Earth (x) m
y-coordinate of object or event in the system S connected to the Earth (y) m
z-coordinate of object or event in the system S connected to the Earth (z) m
Velocity of system S' relative to the system S at rest in the x-direction (V_x) m/s
Velocity of system S' relative to the system S at rest in the y-direction (V_y) m/s
Velocity of system S' relative to the system S at rest in the z-direction (V_z) m/s
Time of event's occurrence in the system S connected to the Earth (t) 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.

Lorentz Transformation of Coordinates Calculator Results (detailed calculations and formula below)
x-coordinate of object or event in the system S' moving at velocity V relative to the system S x' calculations
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' = **x - V_x ∙ t/√*1 - V²_x/c²* 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 - V²_y/c²* 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 - V²_z/c²* 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]

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Discover Physics with free Physics Revision Notes and Physics Calculator: Lorentz Transformation Of Coordinates. This image shows the properties and lorentz transformation of coordinates formula for the Lorentz Transformation Of Coordinates. The Lorentz Transformation of Coordinates Calculator 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

x-coordinate of object or event in the system S' moving at velocity V relative to the system S x' Formula and Calculation

x' = x - V_x ∙ t/√1 - V²_x/c²

y-coordinate of object or event in the system S' moving at velocity V relative to the system S y' Formula and Calculation

y' = y - V_y ∙ t/√1 - V²_y/c²

z-coordinate of object or event in the system S' moving at velocity V relative to the system S z' Formula and Calculation

z' = z - V_z ∙ t/√1 - V²_z/c²

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