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Binoculars Angular-Size Range — result sheet
Estimate the distance to a target of known height from its apparent angular size and binocular magnification.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: θtrue = θapparent/M; range = h/tan(θtrue), converting arcminutes to radians before evaluating.
Angular magnification makes a target appear larger, so the true angle subtended by the target is the apparent angle divided by magnification. With a known height and a small-angle line-of-sight geometry, the calculator estimates the range and also reports the small-angle approximation.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Target height — m; minimum 1.0E-6; maximum 1000000
- Apparent angular height — arcmin; minimum 0.001; maximum 18000
- Binocular magnification — ×; minimum 1; maximum 200
Worked example
| Input | Value |
|---|---|
| Target height | 2 |
| Apparent angular height | 10 |
| Binocular magnification | 8 |
True angular height 1.25 arcmin and range about 5.50 km
Assumptions and limits
- The target height is the dimension spanning the entered angular size and is perpendicular enough to the viewing direction for this geometry.
- Magnification is treated as an ideal angular multiplier; focus, objective diameter, atmospheric clarity, contrast, and eye resolution are not modeled.
- The result is a geometric estimate and not a guarantee that a real observer can identify or resolve the target.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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