A light-year is defined as the distance the light can cover in one year.
The light travels at speed of [tex]c=3 \cdot 10^8 m/s[/tex], and one year converted into seconds is
[tex]1 y = 365 \frac{d}{y} \cdot 24 \frac{h}{d} \cdot 60 \frac{m}{h} \cdot 60 \frac{s}{m}=3.15 \cdot 10^7 s [/tex]
So the distance covered by the light in one year is
[tex]S=vt =(3 \cdot 10^8 m/s)(3.15 \cdot 10^7 s)=9.45 \cdot 10^{15} m[/tex]
And this is the distance that corresponds to one light-year.
