# Applying a z-factor

The z-factor is a conversion factor that adjusts the units of measure for the vertical (or elevation) units when they are different from the horizontal coordinate (x,y) units of the input surface. It is the number of ground x,y units in one surface z-unit. If the vertical units are not corrected to the horizontal units, the results of surface tools will not be correct.

The z-values of the input surface are multiplied by the z-factor when calculating the output surface. If the x-, y-, and z-units are all the same (in feet, for example), the z-factor is 1. This is the default value for the z-factor. For another example, if your vertical z-units are feet and your horizontal x,y units are meters, you would use a z-factor of 0.3048 to convert your z-units from feet to meters (1 foot = 0.3048 meters).

The correct use of the z-factor is particularly important when the input raster is in a spherical coordinate system, such as decimal degrees. It is not uncommon to perceive the output from Hillshade as looking peculiar if the input surface raster is not in a projected coordinate system. This is due to the difference in measurement between the horizontal ground units and the elevation z-units. Since the length of a degree of longitude changes with latitude, you will need to specify an appropriate z-factor for that latitude.

If your x,y units are decimal degrees and your z-units are meters, some appropriate z-factors for particular latitudes are as follows:

Latitude Z-factor 0 0.00000898 10 0.00000912 20 0.00000956 30 0.00001036 40 0.00001171 50 0.00001395 60 0.00001792 70 0.00002619 80 0.00005156

Note that as the range of latitude in your raster data increases, the more approximate the results will be.