This paper describes a mathematical procedure for the direct calculation of reaction orders for typical solution phase reactions. The algorithm described has no dependence on reaction constants that are part of a formal rate expression, for example the rate constant. All that is required is a data set containing a measured reaction rate and a corresponding time interval or a corresponding reaction concentration. From this data set, the reaction order can be directly calculated from a minimum of two data points. By systematic application of the mathematical procedure to a data set, changes in reaction order can be deduced during the course of a reaction, be it integral or non-integral. Such application may be used to characterise complex reaction schemes such as parallel and consecutive reactions or for reactions where there is a change in reaction order. Data simulated from formal rate expressions have been used to illustrate the principles of the analysis and to examine the limitations when used in conjunction with more complex reaction schemes. A procedure of systematic calculation of reaction orders has been developed using a mathematical spreadsheet, MathCad(TM) version 2000 [http://www.mathcad.com].