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Wndsn Shadow Square Calculator

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

By way of using the shadow square on a Wndsn Quadrant, we can obtain information about angles and convert between ratio, tan, arctan, cot, arccot, and angle.

Calculate range.

Calculating shadows.

Example: 8/12 on the shadow square (umbra recta) results in a tangent value (on the slope scale) of 1.5 where arctan(1.5) ≅ 56°.


Determine tan or cot, and arctan, or arccot of a shadow square.


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The horizontal scales are called 'umbra recta', which is Latin for true, or straight shadow and describes the tangent. The vertical scales are named 'umbra versa', from Latin meaning turned, or upright shadow; the cotangent.

Note that cot(x) = 1/tan(x), so cotangent is the reciprocal of a tangent while arctan(x) is the angle whose tangent is x.

See also