Angular Size Calculator
Calculate the angular size (apparent size) of an object from its actual diameter and distance, in degrees, arcminutes, and arcseconds.
Cómo usar esta calculadora
- 1Enter the object's actual diameter.
- 2Enter its distance, in the same unit as the size.
- 3Read its angular size in degrees, arcminutes, and arcseconds.
- 4Compare it to the full Moon (about half a degree) for a sense of scale.
Cómo funciona
Angular size
angular size = 2 × arctan(size ÷ (2 × distance)) for small angles ≈ size ÷ distance (in radians) 1 degree = 60 arcminutes = 3600 arcseconds same unit for size and distance
Angular size, or angular diameter, is how large an object appears from a given distance, measured as the angle its width subtends at the eye rather than its true physical size. An object of a certain diameter seen from a certain distance spans a specific angle in your field of view, found by the trigonometry of a triangle whose base is the object and whose apex is your eye — twice the arctangent of half the object's size divided by the distance. Because it depends on the ratio of size to distance, angular size falls as an object recedes: the same object looks half as wide at twice the distance. For the small angles common in astronomy, the formula simplifies to size divided by distance, giving the angle directly in radians, since the tangent of a small angle nearly equals the angle itself. Angular size is measured in degrees and their subdivisions, arcminutes and arcseconds, which is why telescopes and star charts are described in those units.
Ejemplo resuelto
The Moon is about 3,474 km across and 384,400 km away, so its angular size is 2 × arctan(3474 ÷ 768,800) ≈ 0.518°, or about 31 arcminutes — roughly half a degree. This is why you can just cover the Moon with the tip of your little finger held at arm's length.
Angular Size Calculator: la guía completa
Apparent size versus real size
One of the first lessons of looking at the sky is that how big something appears has little to do with how big it actually is. The Sun is about 400 times wider than the Moon, yet the two look almost exactly the same size in the sky — because the Sun is also about 400 times farther away. This is angular size at work: what your eye registers is the angle an object spans, which depends on the ratio of its true size to its distance, not on either alone. A firefly nearby can blot out a distant galaxy.
This is why angular size is the natural language for describing how things look, especially in astronomy where objects range from nearby planets to unimaginably distant galaxies. Two objects with the same angular size appear equally large, however different their true dimensions. It also explains everyday perspective — why a car looks smaller as it drives away, why distant mountains seem modest until you approach, and why holding your thumb up can cover the Moon. The eye and camera both capture angular size; converting it back to real size requires knowing the distance, which is often the hard part.
Degrees, arcminutes, and arcseconds
Angular sizes in astronomy span an enormous range, from the half-degree discs of the Sun and Moon down to the tiny fractions of an arcsecond that distant stars and planets present, so a hierarchy of units is used. A full circle is 360 degrees; the Moon and Sun are each about half a degree across. For finer measurement, each degree is divided into 60 arcminutes, and each arcminute into 60 arcseconds — the same sexagesimal system used for time. An arcsecond is a very small angle indeed: about the width of a coin seen from several kilometres away.
These units give a feel for what different instruments and eyes can resolve. The unaided human eye can distinguish details down to about one arcminute, which is why the Moon shows visible features but the discs of planets, only a few tens of arcseconds wide, look like points. Telescopes push far beyond this, resolving details of arcseconds or fractions of one, revealing planetary discs, close double stars, and structure in distant objects. When a telescope is described by its resolving power in arcseconds, or a planet's apparent size is quoted for an upcoming close approach, these are angular sizes — the currency of how much detail can be seen.
Using angular size to measure the universe
Angular size is not just a way of describing appearances; it is a tool for measurement. If you know an object's true size, measuring its angular size tells you its distance, and if you know its distance, the angular size tells you its true size. This reciprocal relationship is one of the ways astronomers gauge the cosmos. The physical size of the Moon, for instance, can be worked out from its known distance and its measured angular size, and the same logic scales up to measuring the diameters of stars and the extent of distant galaxies and nebulae.
The technique underpins some of astronomy's classic achievements. Ancient astronomers estimated the sizes and distances of the Moon and Sun from angular measurements during eclipses. Modern astronomers use the angular sizes of 'standard rulers' — objects of known true size — to probe distances across the universe and even the geometry of space itself. On a practical level, knowing an object's angular size tells an observer whether it will fit in a telescope's field of view or a camera's frame, which matters for planning observations of the Moon, planets, and larger deep-sky objects. From the geometry of a triangle, angular size connects what we see to the real dimensions and distances of everything beyond us.
Preguntas frecuentes
What is angular size?
Angular size is how large an object appears — the angle its width spans in your field of view — rather than its true size. It depends on both actual size and distance, so a small nearby object and a huge distant one can look the same size. It's measured in degrees, arcminutes, and arcseconds.
How do I calculate angular size?
Angular size = 2 × arctan(size ÷ (2 × distance)), using the same unit for size and distance. For small angles it's very nearly size ÷ distance in radians. The Moon, 3,474 km across and 384,400 km away, has an angular size of about 0.52°.
Why do the Sun and Moon look the same size?
Because their ratios of size to distance are nearly equal. The Sun is about 400 times wider than the Moon but also about 400 times farther away, so both span roughly half a degree in the sky. This coincidence is why total solar eclipses are possible.
What are arcminutes and arcseconds?
Subdivisions of a degree for measuring small angles. One degree is 60 arcminutes, and one arcminute is 60 arcseconds. The Moon is about 31 arcminutes across; the human eye resolves about 1 arcminute; telescopes reach arcseconds or less, which is why they show planetary detail the eye can't.