metre

SI base unit

Name	Symbol	Quantity
metre	m	length
The metre, symbol m, is the SI base unit of length. The metre is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m s⁻¹, where the second is defined in terms of the caesium frequency Δν_Cs.
Definition
$1 \mspace{4mu} \text{m} \mspace{6mu} = \dfrac{9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770}{299 \mspace{4mu} 792 \mspace{4mu} 458} \mspace{6mu} \dfrac{c}{\Delta \nu _{Cs}}\\ \\ \\ 1 \mspace{4mu} \text{m} \mspace{6mu} \approx 30.663 \mspace{4mu} 318 \mspace{4mu} 988 \mspace{4mu} 498 \mspace{4mu} 369 \mspace{4mu} 762 \mspace{4mu} 191 \mspace{6mu} c \mspace{4mu} {\Delta \nu _{Cs}}^{-1}$

Length

The relation between the speed of light in vacuum, c, and the caesium frequency, Δν_Cs, forms the basis for the definition of the unit of length, the metre.

The definition of the metre implies the exact relation:

$c \mspace{6mu} = 299 \mspace{4mu} 792 \mspace{4mu} 458 \mspace{6mu} \text{m} \mspace{4mu} \text{s}^{-1}$

Inverting this relation gives an exact expression for the metre in terms of the defining constants c and Δν_Cs :

$1 \mspace{4mu} \text{m} \mspace{10mu} = \dfrac{{c}} {299 \mspace{4mu} 792 \mspace{4mu} 458} \mspace{6mu} \text{s}\\ \\ \\ 1 \mspace{4mu} \text{m} \mspace{10mu} = \dfrac{9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770}{299 \mspace{4mu} 792 \mspace{4mu} 458} \mspace{6mu} \dfrac{c}{\Delta \nu _{Cs}}\\ \\ \\ 1 \mspace{4mu} \text{m} \mspace{10mu} = 30.663 \mspace{4mu} 318 \mspace{4mu} 988 \mspace{4mu} 498 \mspace{4mu} 369 \mspace{4mu} 762 \text{...} \mspace{6mu} \dfrac{c}{\Delta \nu _{Cs}}$

The effect of this definition is that one metre is the length of the path travelled by light in vacuum during a time interval with duration of ¹⁄_{299 792 458} of a second.