Vcapmax is the VCC maximum value that the capacitor is charged to.
Vcapmin is the minimum operating voltage you can tolerate before your circuit or component, which is backed up by the capacitor, stops working.
Imax is the maximum current that your circuit will discharge the capacitor.
This can be a constant current or the initial linear current at Vcapmax.The Imax and Vcap values are used to calculate the equivalent resistance of the circuit, which is used in the
equation to calculate the backup time.
From basic electronics, the formula to determine the voltage across a capacitor at any given time (for the
discharge circuit in Figure 1) is: V(t) = E(e-t/RC)
Rearranging this formula for time gives us: t = - log(V/E)(RC)
V is the ending voltage in volts (V)
E is the initial voltage in volts (V)
R is the resistive load in ohms(Ω)
C is the capacitor value in farads 1F=1000 000μF=1000 000 000nF=1000 000 000 000pF
t is the time in seconds
More about super capacitors
A supercapacitor, supercondenser, pseudocapacitor, electrochemical double layer capacitor (EDLC), or ultracapacitor,
is an electrochemical capacitor with relatively high energy density, typically on the order of thousands
of times greater than an electrolytic capacitor. For instance, a typical D-cell sized electrolytic capacitor
may have capacitance in the range of tens of millifarads. The same size electric double-layer capacitor
might reach several farads, an improvement of two orders of magnitude. Supercapacitors usually
yield a lower working voltage in the range 2,5 - 20V. As of 2010 larger double-layer capacitors have capacities
up to 5,000 farads. Also in 2010, the highest available supercapacitor energy density
is 30 Wh/kg, lower than rapid-charging lithium-titanate batteries.
EDLCs have a variety of commercial applications, notably in "energy smoothing" and momentary-load devices.
They have applications as energy-storage devices used in vehicles, and for smaller applications like
home solar energy systems where extremely fast charging is a valuable feature.
Super capacitors are widely used as a backup power source for realtime clock circuits and memory in microcontroller applications for years.
More information in Wikipedia here.