# Lorentz Factor Formula

Diagram shows the fixed frame in 3 dimensional view, with 3 directions x, y and z respectively.

Consider the Moving frame where x’ is moving with primed frame with the velocity v in x direction.

The reference frames coincide at t=t’=0.

${x}’=\frac{x-vt}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$ ${y}’=y$ ${z}’=z$ ${t}’=\frac{t-\frac{vx}{c^{2}}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$

Where,

$\beta =\frac{v}{c}$ $\gamma =\,Lorentz\,factor$ $\gamma =\frac{1}{{{\sqrt{1-\frac{v^{2}}{c^{2}}}}}}$

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