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Unit Conversions · Specialized measurement · Astronomy & extreme scales

Angular Size, Physical Size and Distance Calculator

Solve exact angular diameter, transverse physical size, or line-of-sight distance and compare the result with the small-angle approximation across astronomical and ordinary units.

Unit Conversions · Specialized measurement · Astronomy & extreme scales

Angular Size, Physical Size and Distance Calculator

Private in-browser calculation · explicit models, units, assumptions, and companion outputs

Calculation result

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Enter valid values to see the result.

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Quick guide

How to use this calculator

  1. Choose the astronomical relationship and solve direction first, then keep angles, distances, wavelengths, magnitudes, fluxes, and motion units explicit.
  2. Use exact geometry where supplied and compare it with the small-angle or classical approximation rather than assuming every astronomical scale uses the same model.
  3. Use the companion outputs to reconcile the result, then retain the stated observational and model limits before interpreting a theoretical value as a measured physical property.

Calculation method

How the angular size, physical size and distance calculator works

Keep the exact tangent geometry and the commonly used small-angle relationship together so visitors can see when the approximation is material.

Exact full-angle geometry is physical size = 2 × distance × tan(angle/2). The small-angle approximation is physical size ≈ distance × angle in radians; reverse modes rearrange the exact relationship.

Worked example

Angular Size, Physical Size and Distance example

A 3,474.8 km object at 384,400 km subtends about 0.518° using the exact relationship.

Exact full-angle geometry is physical size = 2 × distance × tan(angle/2). The small-angle approximation is physical size ≈ distance × angle in radians; reverse modes rearrange the exact relationship.

Supported inputs

Precision and limits

Astronomy and model boundary

This is transverse Euclidean geometry using a single distance. It does not infer projection, cosmology, gravitational lensing, extended-object depth, atmosphere, image distortion, or whether an observed boundary represents the physical diameter of interest.

Precision and reporting

Calculations retain working precision and round only for display. Very small and large nonzero values use scientific notation; displayed digits cannot create accuracy, traceability, or observational certainty absent from the entered data.

Category ownership

This collection owns unit-aware astronomy and extreme-scale measurement relationships. Calendar astronomy, orbital dynamics, cosmology, telescope equipment selection, and professional astrometric reduction require separate models and tools.

Privacy

Entered values and results stay in this browser and are not sent to analytics or third parties.

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