Formula: Length Contraction Length / Distance Rest length Relative velocity
$$\Delta x' ~=~ \sqrt{1 ~-~ \frac{\class{blue}{v}^2}{c^2}} \, \Delta x$$
$$\Delta x' ~=~ \sqrt{1 ~-~ \frac{\class{blue}{v}^2}{c^2}} \, \Delta x$$
$$\Delta x ~=~ \frac{ \Delta x' }{ \sqrt{1 ~-~ \frac{\class{blue}{v}^2}{c^2} } }$$
$$\class{blue}{v} ~=~ c \, \sqrt{ 1 ~-~ \left(\frac{ \Delta x' }{ \Delta x } \right)^2 }$$
Length / Distance
$$ \Delta x' $$ Unit $$ \mathrm{m} $$
Length of the body (e.g. a rod) measured by an observer moving relative to this body with velocity \( v \). But it can also simply be the spatial distance between two objects.
Rest length
$$ \Delta x $$ Unit $$ \mathrm{m} $$
Length at rest is the length of a body measured by an observer when the observer is in the body's rest frame. That is, from the observer's point of view, the body is not moving.
Relative velocity
$$ \class{blue}{v} $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$
Relative velocity between the observer and the body.
Speed of light
$$ c $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$
Speed of light is a physical constant and indicates how fast light travels in empty space (vacuum). It has the following exact value in vacuum:
$$ c ~=~ 299 \, 792 \, 458 \, \frac{ \mathrm{m} }{ \mathrm{s} } $$