A common rule of thumb for sizing batteries to solar power relates nominal panel output in Watts to bank capacity in Ah. It is not gospel. It is not a commandment. It is a quick heuristic to understand how your system is biased.
1:1 == 200W solar + 200Ah battery bank. This is generally considered the minimum, as it can work fine in sunny areas with light loads and shallow depths of discharge.1) It may not be enough with heavier use, or in the winter when the sun is low and daylight short. Power rationing may be necessary.
Working backwards, fully charging lead-chemistries from 50% DoD by 1:1 solar requires ~8.45hrs of Full Sun Equivalent on MPPT controllers, or ~9.7hrs FSE with PWM. There is nowhere in the United States that averages 8.45hrs of FSE year around. The highest is Honolulu with an average of 5.96hrs. The highest monthly average is Las Vegas in June (7.69hrs).
2:1 == 200W solar + 100Ah of battery. This slightly overpaneled configuration brings in extra power for heavier loads or for use in areas without much sun.
Working backwards, successfully fully charging lead-chemistries by 2:1 solar requires about 4.25hrs of Full Sun Equivalent on MPPT, and about 4.85hrs FSE with PWM.
On average, this would work in Little Rock, San Francisco, Phoenix, Birmingham, Atlanta, New Orleans, Albuquerque, Tulsa, Las Vegas, San Antonio, Houston, Salt Lake City, and Casper Wyoming. Winters will require power management.
3:1 == 300W solar + 100Ah of battery. This significantly overpaneled configuration generally yields an excess of power, useful in rain, low winter sun, overcast conditions, etc. 'Dwellers in the Pacific Northwest2) may need a 3:1 ratio to meet basic needs.
Working backwards, successfully fully charging lead-chemistries by 3:1 solar requires about 2.83hrs of Full Sun Equivalent on MPPT, and about 3.25hrs FSE with PWM.
On average this this opens up everything but Canada and Anchorage AK.
1:2 == 100W solar + 200Ah of battery. Also known as overbanking), this configuration can work fine in certain configurations:
Outside the above configurations, underpaneling can contribute to battery murder.
Different battery types have different charging requirements: