Angular Size Calculator Formula

Understand the math behind the angular size calculator. Each variable explained with a worked example.

Use the Angular Size Calculator

Formulas Used

Angular Size (radians)

angular_rad = diameter / distance

Angular Size (degrees)

angular_deg = (diameter / distance) * (180 / pi)

Angular Size (arcmin)

angular_arcmin = (diameter / distance) * (180 / pi) * 60

Angular Size (arcsec)

angular_arcsec = (diameter / distance) * (180 / pi) * 3600

Variables

VariableDescriptionDefault
diameterPhysical Diameter(km)3474
distanceDistance to Object(km)384400

How It Works

Angular Size

The angular size (angular diameter) of an object as seen from a given distance.

Small-Angle Approximation

θ ≈ d / D (radians)

where d = physical diameter, D = distance. Multiply by 180/π for degrees, then by 60 for arcminutes or 3600 for arcseconds.

Worked Example

The Moon: diameter 3 474 km, distance 384 400 km.

diameter = 3474distance = 384400
  1. 01θ = 3474 / 384400 = 0.009038 rad
  2. 02Degrees: 0.009038 × 57.296 = 0.5178°
  3. 03Arcminutes: 0.5178 × 60 = 31.07'
  4. 04The Moon is about half a degree across.

Ready to run the numbers?

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