I just bought a car battery charger and multimeter, after a disaster of not being able to start my car recently. The dealer replaced the battery. I've been reading online that a fully charged cold battery should read 12.6 volts. After I charged the battery, it read 13.0 volts. Should I be concerned?
Don't be concerned. You may be seeing what's called "surface charge". It's a chemical effect. You can't really have voltage that's too high. I think that if you come back after a couple of hours, or even press the brake pedal to activate some lights, you will see it come back down to 12.6-12.7V
https://batteryuniversity.com/learn/article/water_loss_acid_stratification_and_surface_charge
No... do not be concerned. The nominal voltage of a storage battery is 12.6 but should be in the range of 12.0 to 13 volts statically sitting there with a full charge.
Trickle chargers that can be left on a battery essentially forever are around 13.8 volts and will cause no harm. That is the voltage pressure necessary to prevent discharging from occurring in the battery due to natural corrosive processes.
If its reading 13 or 13.2 after driving that is completely normal. Nothing to worry about here.
You are all good...
