Full fuel is 56 gal and usable fuel is 53 for c172r. Other than when the fuel indicator is broken, when the fuel indicator indicate red index? Is there any fuel quantity setting to indicate red?
As always, the answer to this question is in the POH. You should always check the specific POH for the aircraft in question but you can usually find one for common aircraft (such as a 172) online. One such example is here.
Under the section on instruments, and specifically "fuel systems"
Fuel quantity is measured by two float-type fuel quantity transmitters (one in each tank) and indicated by two electrically-operated fuel quantity indicators on the left side of the instrument panel. An empty tank is indicated by a red line and the letter E. When an indicator shows an empty tank, approximately 1.5 gallons remain in a standard tank, and 2 gallons remain in a long range tank as unusuable fuel. The indicators cannot be relied upon for accurate readings during skids, slips, or unusual attitudes.
I'm pretty sure the "r" variant in your question is the 172 fitted with long range tanks.