Missile range

what decide missile max range apart from size of missiles , launch speed and altitude :confused:
why the range of PAC-3 is so short :confused: it even have shorter range than the SL-AMRAAM, and half the range of ESSM although it the biggest of the three missiles not to mention it dont even have a warhead and dont have to be agile to intercept agile target like Aim-120 or ESSM

Data for PAC-3:

Length 5.2 m (17 ft 1 in)
Finspan 51 cm (20 in)
Diameter 25 cm (10 in)
Weight 320 kg (700 lb)
Speed Mach 5+
Ceiling 15000 m (50000 ft)
Range 20 km (12 miles)

http://www.astronautix.com/lvs/pac3.htm

ESSM
Weight 620 lb (280 kg)
Length 12 ft (3.66 m)
Diameter 10 in (254 mm)
Warhead 86 lb (39 kg) blast-fragmentation
Detonation
mechanism Proximity fuze
Engine Mk 143 Mod 0 solid fuel rocket
Operational
range 27nm (50 km)
Speed Mach 4+

http://en.wikipedia.org/wiki/RIM-162_ESSM

SL-AMRAAM
Weight 335 pounds (152 kg)
Length 12 feet (3.7 m)
Diameter 7 inches (180 mm)
speed Mach 4
its maximum range that has been cut to 20-mile (33 km) due to the surface launch mode

http://www.deagel.com/Surface-to-Air-Missiles/SL-AMRAAM_a001164005.aspx
https://www.strategypage.com/htmw/htada/20110111.aspx

can the SL-AMRAAM carried by fighter ? i mean they use the same rack as aim-120 right ?

why the SM-2 ER (RIM-67) have shorter range than SM-2 ER (RIM-156) even though it is the same missile with much longer booster ?