What should the voltage readings be at the battery with the engine off and then with the engine running as tested with a volt meter?

 

Well said - "it depends"
A lead acid battery has 6 cells, each with a nominal voltage of 2.1 VDC. That leads one to believe that an unloaded (disconnected) fully charged battery should read 12.6 VDC. Not always the case depending on the individual battery and it's state of charge. As Mr. 8Vette7 said, when you connect any load to the battery, i.e. under hood light, cabin lights, or especially when you turn on your headlights you will see a significant voltage drop. Read the voltage when you are engaging the starter - it is likely to drop to 9 or 10 VDC.

With the car running, the battery voltage reads higher, because the alternator output is set to about 14.5VDC. So you are really measuring the voltage that the regulator inside the alternator is set to. The voltage at the alternator may be slightly higher due to a voltage drop along the length of the cable. When charging, the voltage is set higher than the nominal battery voltage to ensure the battery charges. If your regulator is set too low your battery may never fully charge. Again turn on your headlights with the car running and you may see a voltage drop. Rev your engine and watch it rise.

Batteries start to fail when they are no longer able to deep cycle charge - become severely discharged and lose the ability to be recharged to provide enough amperage to run your system, i.e. work under load. They may read 12+VDC - but measure it when your starter is engaged. If it drops below 9VDC then it is likely on it's last legs.

 

Off, my battery reads 12.9. (Optima red bought last year). On dash it reads 14+ but I have read that reading might not be very accurate.

 

Off=key off. Testing battery with volt meter
14+= on dash gauge with motor running.

 

One thing to do when checking the battery voltage is to make sure that the various timers have shut everything off such as interior lights and the underhood lights. Wait for a minute before checking the battery voltage. 12.9 indicates a fully charged battery but 12.7 to 12.9 is a good range.

A reading above 14 volts for a short time after engine start is fine. Once the alternator brings the battery charge back up, you should see voltage reading around 13.5 to 14 depending on what things are running (lights on, A/C on, radio, wipers, etc.)

You should also check voltage at the alternator to see how close the digital volt display is compared to your VOM.

 

This is an interesting thread as I had the exact same question. With the the ignition off and using a multimeter, I measured 12.86 volts. There was no load that I was aware of with the exception of the security system. The battery is a 5 year old Delco that is usually kept on a maintainer.