Angular Size
Calculator
Results
- Angular size (degrees)
- 0.517924
- Angular size (arcminutes)
- 31.075445
- Angular size (arcseconds)
- 1,864.526712
Astronomy results
| Angular size (degrees) | 0.517924 |
| Angular size (arcminutes) | 31.075445 |
| Angular size (arcseconds) | 1,864.526712 |
formula-map diagram
- Angular size (degrees)
- 0.517924
- Angular size (arcminutes)
- 31.075445
- Angular size (arcseconds)
- 1,864.526712
Astronomical relationship
Formula
θ = 2 arctan(d / 2D)= 0.51792408680334
Note
This result is a simplified model: it applies the displayed textbook formula to the values you entered, assuming ideal spherical bodies, circular orbits, blackbody radiation and perfect optics, and ignoring atmospheric seeing, relativistic corrections beyond those stated, cosmological models and measurement uncertainty. Use published ephemerides and catalogue data for real observations.
More in Astronomy and space
See all →Frequently asked questions
What does angular size measure, as opposed to actual physical size?+
Angular size is how large an object appears from a given viewpoint, measured in degrees, arcminutes, or arcseconds, rather than its true physical dimensions. The same object appears with a smaller angular size the farther away it is, even though its actual size never changes.
How is angular size calculated from an object's actual size and distance?+
For distant objects, angular size (in radians) approximately equals actual size divided by distance, then converted to degrees or arcseconds; both values must use the same length units. This small-angle approximation works well as long as the object is much smaller than its distance.
Why do the Sun and Moon appear to be almost exactly the same size in the sky?+
The Sun's diameter is about 400 times the Moon's, but it's also about 400 times farther away, so their angular sizes happen to nearly coincide at around 0.5 degrees. This remarkable coincidence is exactly what makes total solar eclipses possible.
Does the small-angle approximation break down for very large or very close objects?+
Yes, if the angular size approaches or exceeds roughly 10-15 degrees, the simple size/distance approximation loses accuracy and true trigonometry (like the tangent function) should be used instead. For virtually all astronomical objects, which are extremely far away relative to their size, the approximation is more than sufficient.
What's the difference between an arcminute and an arcsecond?+
A degree is divided into 60 arcminutes, and each arcminute is divided into 60 arcseconds, so there are 3,600 arcseconds in one degree. Astronomers use these finer units because most celestial objects, like planets or distant galaxies, span only a tiny fraction of a degree.