Battery voltage is never stable; it will bounce as the load changes. A Made in China cigarette lighter volt meter isn't a test tool and I wouldn't trust what it tells me for a second.

You need a REAL voltmeter connected to the output of the alternator (positive terminal of battery) if you want a TRUE reading.

Watch this youtube video:
Read the comments; people make good points...if the battery temp is higher or lower than 68 degrees, then "normal" voltage will increase/decrease accordingly.

Most auto parts stores will do this test for free in hopes of selling you a battery or an new alternator.

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with the car off:
I would disconnect the + terminal and read the voltage.
Reconnect the + terminal and read the voltage; should be the same.

Start the car and measure the voltage:
>If the voltage is the same, then the battery is not charging or discharging...it may be fully charged or the alternator output can't match the load...may or may not have a problem.
>Voltage is higher, battery is charging - all is good.
>Voltage is lower, battery is discharging - alternator bad or simply can't meet the load you're demanding (say you had some super power hungry, non stock, item on in the system..1000watt off road lights)

 

Thank you all for your comments!

I finally got the alternator replaced. Now the voltage is nicely around 14.5V all the time - morning, evening, load, no load... the way it should be.