 For a perfect fluid in thermodynamic equilibrium, the stress–energy tensor takes on a particularly simple form

where formula_4 is the mass–energy density (kilograms per cubic meter), formula_61 is the hydrostatic pressure (pascals), formula_62 is the fluid's four velocity, and formula_63 is the reciprocal of the metric tensor.Therefore, the trace is given by

The four velocity satisfies

In an inertial frame of reference comoving with the fluid, better known as the fluid's proper frame of reference, the four velocity is 

the reciprocal of the metric tensor is simply

and the stress–energy tensor is a diagonal matrix

The Hilbert stress–energy tensor of a source-free electromagnetic field is

where formula_70 is the electromagnetic field tensor.The stress–energy tensor for a complex scalar field formula_71 which satisfies the Klein–Gordon equation is
and when the metric is flat (Minkowski) its components work out to be