Battery test
WARNING: This page is about a different car, the 2010 BMW M3, 2009 BMW M3, and 2008 BMW M3. However, it is still accessible from the selected car via links, so may be relevant.
The battery acid density can be used to measure the charge state. However this test produces uncertainty caused by a design-related range of variation. The acid density e.g. for a charged battery is 1.28 kg/l (in the tropical version the acid density is 1.23 kg/l).
Another interference factor is the acid lamination immediately after filling with distilled water.
Battery wear with partially sulfated and/or heavily contaminated plates will also lead to incorrect acid density test results.