The Angular Size Calculator finds how large any object appears at a given distance, in degrees, arcminutes, or arcseconds. Converts freely between angular size, physical dimensions, and distance — essential for astronomy, telescope selection, photography, and optics.
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0.53339221
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32.0035327
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1,920.21196176
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0.00930945
rad
0.53339221
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32.0035327
arcmin
1,920.21196176
arcsec
The Moon and the Sun appear almost identical in size from Earth — yet the Sun is 400 times larger. They look the same because the Sun is also 400 times farther away. This is angular size at work: what matters visually is not an object's actual dimensions but the angle it subtends at your eye. The calculator for angular size converts between actual size, distance, and apparent angular size in any direction — finding any one given the other two.
For an object of physical size d at distance D (measured center-to-center), the angular size θ is:
θ = 2 × arctan(d / 2D) (exact formula)
For small angles (θ ≪ 1 radian, which applies to virtually all astronomical objects), this simplifies to the small-angle approximation widely used in astronomy:
θ ≈ d / D (in radians, when d ≪ D)
Converting to arcseconds: θ″ ≈ 206,265 × d / D. The constant 206,265 is the number of arcseconds in one radian (= 360 × 60 × 60 / 2π). The Moon's angular diameter: d = 3,474 km, D = 384,400 km; θ = 2 × arctan(3474/(2×384400)) = 0.518° = 31.1 arcminutes. Use this online calculator for any object at any distance and in any units.
Building intuition for angular sizes helps interpret telescope views and survey images:
The angular separation calculator computes the angle between two sky positions for the same coordinate system.
Angular size is equally critical in photography and optical instrument design. A camera's field of view (FOV) depends on sensor size and focal length: FOV = 2 × arctan(sensor_size / 2f). A full-frame sensor (36 mm wide) with a 50 mm lens: FOV = 2 × arctan(36/100) = 39.6°. When a telescope is used as a telephoto lens, the same formula applies — a 1,000 mm focal length gives a 2.06° FOV on a full-frame sensor, enough to capture the full Andromeda Galaxy. The angular size of a subject tells the photographer exactly what focal length is needed to fill the frame: f = sensor_size / (2 × tan(θ/2)). The astronomy calculators category covers the complete observational and photographic toolkit.
Angular size measurement is the basis of trigonometric parallax — the fundamental distance measurement technique in astronomy. As Earth orbits the Sun, a nearby star appears to shift against background stars by a parallax angle p (half the total angular shift). The distance in parsecs = 1/p(arcseconds). Hipparcos measured parallaxes to ~1 milliarcsecond precision; Gaia achieves ~10 microarcseconds, enabling precise distances to stars thousands of light-years away. Angular size measurement underpins our entire cosmic distance ladder.
Exact formula: theta = 2 * arctan(physical_size / (2 * distance)), in radians. Convert to degrees by multiplying by 180/pi, to arcminutes by multiplying degrees by 60, to arcseconds by multiplying degrees by 3600. The small-angle approximation (theta = size/distance in radians) is accurate to 0.1% when distance is more than 10x the object size.
Degrees are used for large objects (Moon = 0.5 deg, constellations = tens of degrees). Arcminutes for medium objects (galaxies, clusters, planetary disks = 1-60 arcmin). Arcseconds for small objects (planetary details, stellar diameters, asteroid disks = 0.001-50 arcsec). The diffraction limit of the human eye is about 1 arcminute. Ground-based telescopes achieve 0.5-2 arcsecond resolution; space telescopes and interferometers reach milli- and micro-arcseconds.
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The Sun subtends about 32 arcminutes (0.53 degrees). The Moon's average angular diameter is very similar, enabling total solar eclipses.
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M31 is enormous in the sky but most of its extent is in faint outer regions. The bright visible core spans only about 1-2 degrees.
Angular size is the angle subtended by an object as seen from the observer. It is the apparent size of the object in the sky, independent of actual physical size. A nearby small object can have the same angular size as a distant large one. The Moon and Sun have nearly identical angular sizes despite the Sun being 400x larger and 400x farther away.
For objects much farther away than their physical size, theta (in radians) = physical size / distance. This simplifies calculations significantly. It is accurate to better than 0.1% whenever the distance is more than 10x the object's diameter, which is true for virtually all astronomical objects.
An arcsecond is 1/3600 of a degree or 1/60 of an arcminute. It is the standard unit for small angular sizes in astronomy. A parsec is defined as the distance at which 1 astronomical unit subtends 1 arcsecond. The nearest star (Proxima Centauri) has an annual parallax of 0.77 arcseconds.
Stars other than the Sun are so far away that even the largest have angular diameters of only 0.001-0.05 arcseconds — far below the resolution of normal telescopes. Stellar diameters are measured using optical interferometers (like the VLTI or CHARA array) that achieve milli-arcsecond resolution, or from eclipsing binary star timing.
The Sun is about 400 times larger in diameter than the Moon, but it is also about 400 times farther away. This remarkable coincidence means their angular diameters are nearly equal (about 0.5 degrees), allowing total solar eclipses where the Moon exactly covers the Sun's disk. This coincidence is not permanent — the Moon is slowly receding and will eventually be too small to cover the Sun.
Angular resolution is the minimum angular separation a telescope can distinguish as two separate objects. For a perfect circular aperture, the Rayleigh criterion gives theta = 1.22 * wavelength / aperture. A 100mm telescope in visible light (550 nm) has a theoretical resolution of about 1.4 arcseconds. Atmospheric seeing limits ground-based telescopes to about 0.5-2 arcseconds.
Magnification multiplies the apparent angular size of an object. A 50x telescope makes the Moon appear 50 times larger in angle, from 0.5 degrees to 25 degrees. The telescope's field of view must be larger than the object's angular size for the entire object to fit in view.
In cosmology, very distant objects are affected by the expansion of the universe. The angular diameter distance D_A relates physical size to observed angular size: theta = size / D_A. For very distant objects (redshift > 1), D_A actually decreases with increasing distance due to cosmic expansion, meaning very distant galaxies can appear larger than intermediate-distance ones.
One light-year = 9.461 x 10^12 km. One parsec = 3.086 x 10^13 km = 3.26 light-years. For example, the Andromeda Galaxy at 2.537 million light-years = 2.4 x 10^19 km. Enter distances in km for this calculator; multiply light-years by 9.461 x 10^12 or parsecs by 3.086 x 10^13.
The largest angular objects visible to the naked eye include the Milky Way (the band of the galaxy spans 360 degrees in galactic longitude), the Large Magellanic Cloud (about 10 degrees), the Andromeda Galaxy (about 3 degrees in its full extent), and the Zodiacal Light (spans about 180 degrees). The Sun and Moon are each about 0.5 degrees.
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