How this calculator works
The target is assumed perpendicular to the viewing direction and centred on the optical axis. Two right triangles relate its full angular height to its physical height. For narrow angles, distance is approximately height divided by angle in radians. A reticle marked in military mils may use a different circle subdivision from a milliradian; convert its calibration first.
Formula
R = H/[2 tan(α/2)]; H = 2R tan(α/2); α = 2 atan[H/(2R)]. For small α, R ≈ H/α.
Worked example
A 2 m target subtending 4 mrad is about 500 m away. A 2 m object spanning 90 degrees would be 1 m from its centre plane.
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Frequently asked questions
Do binocular magnification numbers give range?
No. Magnification alone does not supply angular size; a calibrated reticle or another angular measurement is needed.
What happens if the height is uncertain?
Range changes in direct proportion to the assumed target height.
Can I use a tilted object?
Its projected height is smaller. Use the size perpendicular to the line of sight to avoid overestimating range.