# Slant Range

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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 uses both the law of sines and cosines.   In the obtuse triangle below:

• b = Re + sA
• a = Re + oA
• c is the slant range
• CA is the Earth Central Angle
• BA is the subtended angle (β)
• AA is elevation angle (α) + 90°

where:

 a/(sin("AA")) = b / (sin("BA")) = c / (sin("CA"))

therefore:

c = sqrt( a^2 + b^2 - 2a*b*cos(CA) )