Computing Slant Ranges

(Created 25 September 2009)
(Revised April 2024)

Slant range is very important for calculating weapons effects against airborne or submerged targets, as well as ranges for sensor systems, because the targets are not on the same plane as the weapon/sensor itself.

The Slant Range Equation is:

Or alternately:

R_S = SQRT (R_G² + R_A²)

Where:

R_S = Measured (Slant) Range to Target
R_G = Range to Target on a Flat Plane
R_A = Target's Altitude/Depth

All of the units can be in any unit of measurement (feet, yards, rods, meters, etc) as long as all three ranges are in the same unit of measurement!

You can't mix and match units of measurements here.

EXAMPLE:

A destroyer is 4,000 yards from a submarine which is at a 500 foot depth. What is the slant range line of sight for the destroyer's bow-mounted sonar to the submarine?

First, we convert from the submarine's depth from feet to yards (500 feet = 166.6 yards), and then begin the math:

(4,000 yards² + 166.6 yards²) = 16,027,756

SQRT(16,027,756) = 4,003.47 yards.

Thus, the LOS distance for the destroyer's sonar to the submarine is 4,003.47 yards.

Pre-Built Calculator

Target Range (flat plane)
Target Altitude/Depth (Difference from flat plane)

Slant Range