The  and pH of a solution are related by the Nernst equation as commonly represented by a Pourbaix diagram .  explicitly denotes  expressed versus the standard hydrogen electrode (SHE). For a half cell equation, conventionally written as a reduction reaction (i.e., electrons accepted by an oxidant on the left side):
The equilibrium constant  of this reduction reaction is: 
where curly braces { } indicate activities (), rectangle braces [ ] denote molar or molal concentrations (),  represent the activity coefficients, and the stoichiometric coefficients are shown as exponents. 
Activities correspond to thermodynamic concentrations and take into account the electrostatic interactions between ions present in solution. When the concentrations are not too high, the activity () can be related to the measurable concentration () by a linear relationship with the activity coefficient (): 
The half-cell standard reduction potential  is given by
where  is the standard Gibbs free energy change,  is the number of electrons involved, and  is the Faraday's constant. The Nernst equation relates pH and  as follows:
In the following, the Nernst slope (or thermal voltage)  is used, which has a value of 0.02569... V at STP. When base-10 logarithms are used,  V &lambda; = 0.05916... V at STP where &lambda; = ln[10] = 2.3026. 
This equation is the equation of a straight line for  as a function of pH with a slope of  volt (pH has no units). 
This equation predicts lower  at higher pH values. This is observed for the reduction of O into HO, or OH, and for reduction of H into H.  is then often noted as  to indicate that it refers to the standard hydrogen electrode (SHE) whose  = 0 by convention under standard conditions (T = 298.15 K = 25 °C = 77 F, P = 1 atm (1.013 bar), concentrations = 1 M and thus pH = 0).