Area ratio is the cross sectional area of the nozzle exit divided by the cross sectional area of the nozzle throat. A higher area ratio means the nozzle will be larger and heavier and the exhaust velocity will be higher. Engines optimized for high thrust will have lower area ratios than engines optimized for high exhaust velocity. The engines with the highest ratio would be those that operate in vacuum and don't need high thrust, like those to boost spacecraft after they are in orbit and have plenty of time to accelerate.

An area ratio of four is typical for a rocket operating at sea level. An area ratio of forty is typical for a rocket operating in vacuum. Given k and the pressure ratio the area ratio can be calculated.

k = 1.21
mach = sqrt( 2.0 / ( k - 1.0 ) * ( pow( pressure ratio, 1.0 - 1.0 / k ) - 1.0 ) )

area ratio = pow( ( 1.0 + ( 0.5 * k - 0.5 ) * mach * mach ) / ( 0.5 * k + 0.5 ), ( k + 1.0 ) / ( 2.0 * k - 2.0 ) ) / mach
 
 

This is used in bipropellant rocket, tripropellant rocket, pumped rocket and rocket cost.
 
  Rocket