This report describes the FOI3-method. The method calculates emissions and fuel burn from aircraft. This method is tailored to deal with a large amount of data (typically emission inventories for a year of traffic at many airports). The calculated emissions are CO2, CO, HC (divided into CH4 and NMVOC), NOX, N2O and SO2. The FOI3 method calculates total emissions and fuel burn for each segment of the flight and can be used to calculate the so called LTO cycle (Landing and Take Off cycle below 3000 feet) or for the entire flight. It is easy to allocate the output to individual aircraft types or airports or in different categories like international or domestic flights. In this report we present the methodology, emission sources, requirements on input data and an error estimate of the FOI3 method. This report replaces earlier report (FOI-R-1625--SE) in which the older FFA2 method was described.