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Q:  What power (wattage) rating is required for my RS-485/RS-422 network termination

A: In most applications a 1/4 Watt is sufficient, but in many cases a 1/8 Watt or 1/10 Watt can be used.

Analysis based on the RS-485 specification and typical 3.3V and 5V powered RS-485 transceivers with a standard 120Ω differential termination resistor.

The RS-485 specification includes differential output voltage specifications under full load, and unloaded. 
VOUT loaded (54Ω) ±1.5V
VOUT unloaded ±5V

For worst case resistor power dissipation, consider the RS-485 differential driver output voltage specification under load.  The RS-485 driver outputs are complementary with one driving low while the other drives high.  Ideally the driver outputs are rail-to-rail, so they drive from 0V to VCC.   In reality there is some voltage drop from the rails due to the RDS_ON of the CMOS output MOSFETs. 

An industry standard RS-485 transceiver such as MAX485 provides differential output drive voltage of 2V (minimum) with 50Ω load, and 1.5V (minimum) and 5V (maximum) with 27Ω load.   The 5V maximum specification would only occur when the output drivers have zero voltage drop, and would be an ideal case.   In reality, the actual output voltage will be somewhere between the 1.5V minimum, and 5V maximum. 

Even so, if we take the 5V maximum across a 120Ω termination resistor, the power dissipated in the resistor would be P = V x (V/R) = 5V x 5V / 120Ω = 0.208W.  So a 1/4 Watt resistor would be the largest size needed under worst case conditions.

Assume the output drive will more typically be less than 4V, reducing the power dissipation to P = 4 x 4 / 120 = 0.133W, and a 1/8 Watt resistor (0.125W) would not quite meet the requirement, so a 1/4 Watt still would be better.  

For a 3.3V powered RS-485 transceiver, the output drive will be less than 3.3V which reduces the power dissipation to P = 3.3 x 3.3 / 120 = 0.091W, and a 1/10 Watt resistor would easily meet the requirement.

If the system is running at a hot ambient temperature > +70°C, then temperature derating of the resistor should also be considered.  It would be good to go with a larger case size to allow more margin under these conditions.

 
Surface Mount Resistors and Power Rating
Case SizePower Rating (W)
06031/10
08051/8
12061/4