Angular Size Calculator
Enter an object's real size and its distance to find its apparent angular size, the angle it spans in your view, in degrees, arcminutes and arcseconds.
How to use the angular size calculator
- Enter the object's real size (its diameter or width).
- Enter the distance to it, using the same unit as the size.
- Read the angular size in degrees, arcminutes and arcseconds.
Examples
Apparent size of the Moon
size = 3474 km, distance = 384,400 km
about 0.518 degrees, roughly 31 arcminutes
A 2 m object at 1000 m
size = 2 m, distance = 1000 m
about 0.1146 degrees
Frequently asked questions
What is angular size?
Angular size, or angular diameter, is the angle an object appears to span when viewed from a distance. A nearer object of the same size looks larger.
What is the angular size formula?
theta = 2 x atan(size / (2 x distance)). The size and distance must use the same unit, and the result is an angle that can be shown in degrees.
What are arcminutes and arcseconds?
They subdivide a degree. One degree is 60 arcminutes, and one arcminute is 60 arcseconds, so one degree equals 3600 arcseconds.
Why is the Sun and Moon's angular size about half a degree?
Both span roughly 0.5 degrees from Earth, which is why a total solar eclipse works: the Moon almost exactly covers the Sun's disc.
Can I use any units for size and distance?
Yes, as long as both use the same unit. Only the ratio of size to distance matters, so kilometres, metres or miles all give the same angle.
Related tools
Parallax Distance Calculator
Calculate the distance to a star from its parallax angle. Distance in parsecs is 1 divided by the parallax in arcseconds, plus light years and AU.
Telescope Magnification Calculator
Calculate telescope magnification from focal lengths, plus max useful power, exit pupil and focal ratio from your aperture. Free astronomy optics tool.
Light Travel Time Calculator
Calculate how long light takes to cross any distance. Enter kilometres, AU, light years, parsecs or miles to get seconds, minutes, hours, days and years.
555 Timer Calculator
Calculate 555 timer astable frequency, period, high and low times and duty cycle from R1, R2 and the timing capacitor. Free oscillator design helper.
Absolute Humidity Calculator
Calculate absolute humidity in grams of water vapor per cubic meter from air temperature and relative humidity. Fast, free and works in your browser.
Allele Frequency Calculator
Find allele frequencies from genotype counts. Enter the number of AA, Aa and aa individuals to get the A and a allele frequencies and allele totals.