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COMPENDIUM INCLINATION MEASUREMENT
WYLER AG, WINTERTHUR / SWITZERLAND

1.3 UNITS IN INCLINATION MEASUREMENT

FOR LARGE INCLINATIONS FROM 5...10 DEGREES THE FOLLOWING UNITS ARE NORMALLY USED:
• x.xx Rad radian
• xxxx.xx mRad milliradian
• xxx.xxx° DEG degree
• xxx° xx‘ DEG degree / minutes
• xx° xx‘ xx“ DEG degree / minutes / seconds
• xxx.xxx GON gon
• xxxx.xx A%o artillerie-permille

FOR SMALLER INCLINATIONS UP TO 5...10 DEGREES THE FOLLOWING UNITS ARE NORMALLY USED:
• xxx.xxx mm/m mm per m (μm/m)
• xx.xxxx “/10“ inch per 10 inch
• xx.xxxx “/12“ inch per 12 inch
• xxxx.xx mRad milliradian
• xxxx.xx μRad microradian
• xxx.xxx mm/REL mm in relation to the relative base
• xx.xxxx “/REL inch in relation to the relative base
• xxxx.xx %o permille
• xxxx‘ xx“ DEG minutes / seconds
• xxxxx.x“ DEG seconds
• xxx.xxx GON gon
1.4 RELATIONSHIP BETWEEN DEGREES/ARCMIN AND μm/m

With an inclination measuring instrument not only an inclina-
tion can be determined but also, related to the base length of
e.g. 1 m, the heights of a point (topography of a surface) may be
defined. This fact and the simple use of an electronic inclination
measuring instrument allows the efficient measuring of machine
tool guideways and surfaces in the range of micrometers.
In our example, the inclination  is expressed as a height H in
relation to base length R, which is represented by one meter. The
corresponding trigonometric function between the height H and
the base length R is tangent.

Trigonometric function:
INCLINATION a defined as a height ”H” related to Height “H“ = base line “R“ * tan 
base line ”R”, for instance in [mm/m] or [μm/m]
Assumption: inclination  = 1 arcsec
Height “H“ = Height “R“ * tan 
H Height “H“ = Height of 1m * 0.000004848
a Height “H“ = 0.000004848 m = 4.848 m

R Accordingly, an inclination of 1 arcsec
corresponds to an inclination of 4.848 μm/m
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