From the quantum statistics of a completely degenerate electron gas (all the lowest quantum states are occupied), the pressure and the density of a white dwarf are calculated in terms of the maximum electron momentum standardized as , with pressure  and density , where
 is the mean molecular weight of the gas, and  is the height of a small cube of gas with only two possible states. 
When this is substituted into the hydrostatic equilibrium equation
where  is the gravitational constant and  is the radial distance, we get
and letting , we have
If we denote the density at the origin as , then a non-dimensional scale
gives
where . In other words, once the above equation is solved the density is given by
The mass interior to a specified point can then be calculated
The radius-mass relation of the white dwarf is usually plotted in the plane -.