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Wndsn Expedition Team

Ex Mensura, Scientia

Wndsn Range Calculator

High-precision range calculator. Companion to Wndsn Telemeters: Low tech, high utility graphical distance & altitude computers from the Wndsn applied science lab.

By way of using a Wndsn Quadrant or Telemeter measuring degrees or a hairline graticule measuring mil or moa or any other instrument or technique that returns the angular size of a known object, we can determine the distance to that object.

Calculate range.

The angular relationship between height and distance.

Input

Determine distance d (use any unit (cm, mm, inches, etc.) for s, at angular size α)
Reset

Results

  • Size of the object observed: s = 30
  • Angular size: α = 0.0286 degrees or 0.5 MIL (MRAD) or 0.5093 MIL (NATO-MIL) or 1.7189 MOA
  • Distance multiplier: d = s · 1/tan(0.0286°) = s · 1999.9998
  • Approximate distance: d = 59999.995

The display precision set is .4. To change that, edit the variable &digits=x in the URL where 0 <= x <= 9.

Explanation

[Load sample values (JSON) (XML) (CSV).]

Compare MIL vs. MRAD vs. NATO-MIL.

d = s · 1/tan(α)
  • d = 30 · 1/tan(0.0286°)
  • (We have one angle (0.0286°) and the Opposite side (30), and want to determine the Adjacent side. According to SOHCAHTOA, we need to use Tangent.)
  • tan(0.0286°) = opposite/adjacent
  • Thus: 30/d = tan(0.0286°)
  • Switching sides: d/30 = 1/tan(0.0286°)
  • Multiplying both sides by 30: d = 59999.995
  • (The small angle approximation for skinny triangles shows that the angle in radians approximates to the sine of the angle (for small angles, the hypotenuse is about equal to the adjacent); hence, the larger the angle, the bigger the difference between 1/sin(α) and 1/tan(α).)

Reference

1        rad =  57.3     deg
6.2832   rad = 360       deg = 6283.2   mil = 21,600     minutes (moa)
0.017453 rad =   1       deg =   17.453 mil =     60     minutes (moa)
                 0.0573  deg =    1     mil =      3.438 minutes (moa)
                 0.05625 deg =    1 natomil

Radian, degrees, mrad, NATO-MIL, and MOA.

See also