There are simple approximations for the error function that are adequate for engineering calculations and for incorporation into spreadsheet programs. For quick calculations using a hand calculator, the error function can be broken down piecewise using the following equations:
Using the polynomial solution, carburization profiles were calculated and are shown in Figure 2. These profiles were determined for a 1022 plain carbon steel held at 927°C (1700°F) with a carbon potential of 1.1 weight percent. The diffusivity was calculated from the presented equation, where the absolute temperature (T) is measured in degrees Kelvin.