Couloumb’s inverse square law gives the relationship between the charges q₁ and q₂ which are at a distance of r between them. By Couloumb’s law,

Force between the charges F = k q₁q₂ / r²

Hence, k = Fr² /  q₁q₂

 The unit for F is Newton, r is metre and q is coulomb.

Hence, unit for k is N m² / c² = N m^{2 c-2}