Stagnation temperature can be derived from the First Law of Thermodynamics.  Applying the Steady Flow Energy Equation
 and ignoring the work, heat and gravitational potential energy terms, we have:
where:
: mass-specific stagnation (or total) enthalpy at a stagnation point
: mass-specific static enthalpy at the point of interest along the stagnation streamline
: velocity at the point of interest along the stagnation streamline
Substituting for enthalpy by assuming a constant specific heat capacity at constant pressure () we have:
or
where:
: specific heat capacity at constant pressure
: stagnation (or total) temperature at a stagnation point
: temperature (or static temperature) at the point of interest along the stagnation streamline
: velocity at the point of interest along the stagnation streamline
: Mach number at the point of interest along the stagnation streamline
: Ratio of Specific Heats (), ~1.4 for air at ~300 K