We have a slab on grade with radiant heat with 4 inches of eps insulation under the slab. I have a Persian rug and want to get the best pad for this situation. I plan to go with felt but not sure to go with 3/8 or 1/2 inch thickness. The rug is 18'x 12ft so no concern about rug moving so no need for griping properties. Is this the best material for a pad considering the radiant. I assume the pad and rug will act as a thermal mass also.What if any effect on the heating? The addition has been in use w/o the rug and has worked out well. Is felt the best material vs memory foam or composite. Wool is very expensive.

The thermal mass of wool is completely inconsequential (too low to matter),but the R-value is. The thicker the pad, the more insulation there is between the radiator (the floor) and the room, which means the floor has to be warmer to deliver the same amount of heat into the room, raising the water temp requirements.

Worse case...assume the area rug blocks 100% of the upward heat in the area it occupies. You know the rug area and the heated room floor area. So what percentage of the room floor area is no longer available for heating? If this is a small percentage, no worries. The original design should have included some percentage of blocked heated room floor area to provide design margin for exactly this sort of thing.

A 1/4" commercial pad--solid, not waffle--presents the least resistance to heat transfer and is generally the best choice for rug or carpet longevity since it allows less deflection. When one part of the floor is covered the uncovered area naturally allows for greater heat transfer and if the system calls long enough the surface area for the rug and adjoining floor are often the same.

If only that were true...we could put heavy carpet over most of the HR floor emitter area and all would be nice and cozy and well. Unfortunately, that is not true...

If some portion of the HR floor emitter area is blocked, the remaining HR floor emitter area surface temperature has to become higher in order to provide sufficient room heat gain to offset the room heat loss at the same duty cycle. There comes a point that even if the duty cycle becomes 100%, it would be impossible for the HR floor emitter to keep up without the remaining HR floor emitter area surface temperature exceeding the maximum comfortable barefoot temperature (85F for most rooms and 90F for bathrooms). So the system should have been designed to allow for some heat blockage (typically 10-20%) while still maintaining an acceptable floor surface temperature at the design indoor/outdoor temperatures.

By the way, higher required duty cycle and higher required supply water temperature for a given indoor/outdoor temperature design implies lower heating system efficiency. Essentially what Dana correctly originally explained...

As I said.

The need for a room-by-room heat load--Manual 'J' based radiant specific software being the industry standard, will tell the whole story. In the worst case the ambient temperature may fall below the thermostat setting and the exposed surface area may rise above the arbitrary 85F set by the industry. I have designed perimeter systems, including the one in my shop, wherein the the perimeter is heating room, leaving the field open for anchoring machinery, car lift etc.

The "acceptable" floor surface temperature is only relevant to the areas people walk.