From the equivalent circuit it is evident that the current produced by the solar cell is equal to that produced by the current source, minus that which flows through the diode, minus that which flows through the shunt resistor:
where
*I, output current (ampere)
*I, photogenerated current (ampere)
*I, diode current (ampere)
*I, shunt current (ampere).
The current through these elements is governed by the voltage across them:
where
*V, voltage across both diode and resistor R (volt)
*V, voltage across the output terminals (volt)
*I, output current (ampere)
*R, series resistance (Ω).
By the Shockley diode equation, the current diverted through the diode is:
where
*I, reverse saturation current (ampere)
*n, diode ideality factor (1 for an ideal diode)
*q, elementary charge
*k, Boltzmann constant
*T, absolute temperature
* the thermal voltage. At 25 °C,  volt.
By Ohm's law, the current diverted through the shunt resistor is:
where
*R, shunt resistance (Ω).
Substituting these into the first equation produces the characteristic equation of a solar cell, which relates solar cell parameters to the output current and voltage:
An alternative derivation produces an equation similar in appearance, but with V on the left-hand side. The two alternatives are identities; that is, they yield precisely the same results.
Since the parameters I, n, R, and R cannot be measured directly, the most common application of the characteristic equation is nonlinear regression to extract the values of these parameters on the basis of their combined effect on solar cell behavior. An online simulator to extract the circuit parameters can be found at SolarDesign. 
When R is not zero, the above equation does not give the current I directly, but it can then be solved using the Lambert W function:
When an external load is used with the cell, its resistance can simply be added to R and V set to zero in order to find the current.
When R is infinite there is a solution for V for any  less than :
Otherwise one can solve for V using the Lambert W function:
However, when R is large it's better to solve the original equation numerically.
The general form of the solution is a curve with I decreasing as V increases (see graphs lower down). The slope at small or negative V (where the W function is near zero) approaches , whereas the slope at high V approaches .