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Angular size calculator

The Sun and the Moon both subtend about half a degree from Earth, which is the coincidence that makes total eclipses possible.

Angular size
0.517 924degrees
≈ Rounded Angular size
In arcminutes
31.0754
In arcseconds
1864.527
In radians
0.009 039 480 6
Small-angle approximation
1864.539 arcseconds
Compared with the full Moon
0.9997
Show the working
  1. Actual size = 3474.8
  2. Distance = 384 400
  3. In radians = 2 * atan(3474.8 / (2 * 384 400)) = 0.009 039 48
  4. Angular size = deg(0.009 039 48) = 0.517 924
  5. In arcminutes = 0.517 924 * 60 = 31.0754
  6. In arcseconds = 0.517 924 * 3600 = 1864.53
  7. Small-angle approximation = 3474.8 / 384 400 * 206264.80624709636 = 1864.54
  8. ratio = 384 400 > 0 ? 3474.8 / 384 400 : 0 = 0.009 039 54
  9. Compared with the full Moon = 0.517 924 / 0.5181 = 0.999 66

Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.

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    The formula

    • angular size = 2 arctan(size / (2 x distance))
    • small-angle approximation: arcseconds = 206 265 x size / distance

    206 264.806 is the number of arcseconds in a radian, which is where the small-angle constant comes from.

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