This article is from the Car Audio FAQ, by Ian D. Bjorhovde (email@example.com) with numerous contributions by others.
Before installation, it's often difficult to predict whether or not a
capacitor will be beneficial to you. It's generally best to install
the audio equipment prior to making the determination, so that you can
address which symptoms need to be remedied and assess the severity of
the symptoms. This will not only help you decide whether or not you
need a capacitor, but also how much capacitance would be beneficial.
The most common symptom in need of added capacitance is headlight
dimming (and sometimes dimming of the interior/dash lights). It's
caused by a drop in system voltage associated with excessive current
draw. While there may indeed be several loads drawing substantial
amounts of current from the electrical system (eg. heat, AC, and so
forth), it's usually the transient draws that best manifest themselves
in noticeable dimming. This is partly because our visual systems are
most sensitive to detecting rapidly changing intensity levels rather
than steady absolute differences.
Once you've assessed whether or not the dimming is noticeable (and
sufficiently annoying), you must decide whether a capacitor is
warranted or if you'd be better served by upgrading the alternator.
After initially having your alternator and battery checked out (some
places will do this for free), the choice should be based on the
severity of the dimming.
A commonly-used estimate for determining the appropriate size capacitor
is 1F/kW (one farad per kilowatt). For example, a system running at
300W would need a 0.3F (or 300,000uF) capacitor. However, there are
several variables at play here, including the capabilities of the
vehicle's electrical system (which generally varies from idle to higher
RPMs), the efficiency of the amplifiers, and the listening habits of
the user (ie. the tone controls and the type of music). These factors
should all be considered when making the determination. Moreover, the
voltage drop can be so severe that added capacitance is nothing more
than a band-aid. That is, even several Farads of capacitance would not
be able to sustain the voltage for as long as the drop persists. This
is when an alternator upgrade may be in order.