# Slant Range

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Equation / Last modified by KurtHeckman on 2019/05/17 14:12
R =
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KurtHeckman.Slant Range
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The Slant Range calculator computes the slant range (R) from a ground station to an object (satellite or aircraft) based on the station and object altitudes and the elevation angle (α).

INSTRUCTIONS: Choose units and enter the following:

Slant Range (R):  The range is returned in kilometers.  However this can be automatically converted to compatible units via the pull-down menu.

#### The Math / Science

The formula for the slant range is:

 R = sqrt( (A*cos(α))^2 + r^2 - A^2) - A * cos(α)

where:

• R is the slant range
• A is the distance from the center of the Earth to the station (A = Re + sA)
• r is the distance from the center of the Earth to the object (r = Re + oA)

One can also compute the Slant Range using Position Vectors.