Fuel requirement is one of the most important issues in aircraft performance. For an aircraft of a given mass, flying in an atmosphere where temperature is a monotonically decreasing function of pressure, there is one Mach number and flight level (FL) pair for which the specific air range (SAR), i.e. the distance travelled through the air per unit mass of fuel consumed, is a maximum. Specific air range is directly proportional to the range parameter, which is the product of the overall engine efficiency and the airframe lift-to-drag ratio. During the aircraft design process, the optimum value of the range parameter is fixed at a specific ‘design’ mass in a specific ‘design’ atmosphere. This ‘design optimum’ condition is a characteristic of the aircraft and engine combination, occurring at a particular Mach number and flight level pair. However, in routine operations, the aircraft mass and the atmospheric characteristics will rarely, if ever, coincide with the design conditions. Consequently, in general, the operational optimum Mach number and flight level pair will not be the same as that at the design optimum. The primary purpose of this analysis is to find the general relationship between the operational and the design conditions. In performance calculations, it is often assumed that, if the Mach number and lift coefficient are constant, the range parameter is also constant. This leads to the well-known ‘cruise climb’ trajectory for ‘maximum’ range and, for the whole flight, the classical Breguet range equation for the required trip fuel. However, to maintain a constant lift coefficient, the aircraft must climb as mass reduces and, depending upon the relationship between temperature and pressure in the atmosphere, its Reynolds number changes. It is shown that these Reynolds number changes can alter the range parameter by several percent as the flight progresses, and the standard Breguet equation may produce significant errors in the trip fuel estimation. Therefore, a completely general formulation of the range equation is presented. The well-documented, open-source, Poll-Schumann aircraft performance model is used to provide data for a wide range of operating conditions. Tabulated coefficients are provided to allow operational estimates to be made for 71 aircraft types and variants. These values are best estimates based upon information available in the public domain.