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COMPENDIUM INCLINATION MEASUREMENT
WYLER AG, WINTERTHUR / SWITZERLAND

1.5 WHAT IS A mm/m?

a = 1 μm/m h = 1 μm

a 1 μm/m = 1 mm/km
L = 1 m
It is quite difficult to imagine an inclination of the size of 1 μm/m. Using a small mathematical relation it
becomes more imaginable. By multiplying the baselength “L” and the height “h” by a factor of 1000, the
relation remains the same, L=1km and h=1 mm (1 mm/km). This way, it is much easier to imagine an
inclination of 1 μm/m. As an illustration, a human hair has a diameter of 50...70 μm.
1.6 WHAT IS A RADIAN?

The radian is the standard unit of angular measure, used in many areas of mathematics. It describes the
plane angle subtended by a circular arc as the length of the arc divided by the radius of the arc. The unit
radian is considered an SI derived unit. One radian is the angle subtended at the center of a circle by an arc
that is equal in length to the radius of the circle.
As stated, one radian is equal to 180°/ degrees, therefore:
1 Rad = 360° / 2= 180° = 57.29577°
1 mRad = 0.05729° = 3‘ 43,77“ arc length =
1 μRad = 0.206“ = ca. 1 μm/m radius
The unit radian (symbol: Rad) has the great advantage that
this unit can be used from 0 to 360°. Also for the proces-
sing in the analysis software, this unit has great benefits. It
is obvious that the processing of a single number is easier
than processing units such as degrees / minutes / seconds.
The conversion to other units is carried out via mathematical
libraries that are part of the application software.
For the output of values at the instruments and interfaces
like digital display, transceivers/converters and so on WYLER AG, always used radians [Rad]. The conver-
sion in the desired unit is available in the display device or software.
Important: 1 μRad = 1 μm/m is only valid in the range of very small inclinations (angles)!

1.7 CORRELATION BETWEEN THE MOST COMMON UNITS (SI)
μm/m mm/m arcsec arcmin degree mRad Rad
1 μm/m 1 0.001 0.20627 0.00344 5.730 10 -5 0.001 1 10 -6
1 mm/m 1,000 1 206.265 3.43775 0.0573 1 9.99 10 -4
1 arcsec 4.848 0.00485 1 0.01667 2.778 10 -4 0.00485 4.848 10 -6
1 arcmin 290.89 0.29089 60 1 0.01667 0.29089 2.909 10 -4
1 degree 17,455.1 17.46 3,600 60 1 17.45 0.01745
1 mRad 1,000 1 206.26 3.43775 0.0573 1 0.001
1 Rad 1.557 10 6 1,557 206,264.8 3,437.75 57.3 1,000 1
Important: 1 μRad = 1 μm/m is only valid in the range of very small inclinations (angles)!
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