Ex Mensura, Scientia

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.*

- 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
`1/tan(0.0286°)`

:`d = 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`

.

[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).)