Angular Size Calculator
Calculate how large a celestial object appears in the sky given its physical diameter and distance. Perfect for comparing the apparent sizes of planets, moons, nebulae, and galaxies.
About this calculator
Angular size (also called angular diameter) describes how large an object appears from a given vantage point, measured in degrees, arcminutes, or arcseconds. For objects much smaller than their distance, the small-angle approximation holds: θ (arcseconds) = (physical_size / distance) × (180 / π) × 3600. Here physical_size and distance must be in the same units (e.g., both in km), and the multiplication by (180/π) × 3600 converts radians to arcseconds. One arcsecond is 1/3600 of a degree. The Moon and Sun both subtend about 1800–1900 arcseconds (~0.5°), which is why total solar eclipses are possible. The formula breaks down when the object subtends a large angle (> a few degrees), requiring the exact formula θ = 2 × arctan(size / 2d).
How to use
Find the angular size of Jupiter when it is 628 million km from Earth. Jupiter's equatorial diameter is 142,984 km. Enter 142,984 km as Physical Diameter and 628,000,000 km as Distance. The calculator computes: θ = (142,984 / 628,000,000) × (180 / π) × 3600 = 0.00022768 × 57.2958 × 3600 ≈ 46.9 arcseconds. Jupiter therefore appears about 47 arcseconds wide — large enough to show cloud bands in a small telescope.
Frequently asked questions
How do I calculate the angular size of the Moon in arcseconds?
The Moon's average diameter is 3,474 km and its average distance is 384,400 km. Applying the formula: θ = (3,474 / 384,400) × (180 / π) × 3600 ≈ 1,870 arcseconds, or about 31.2 arcminutes (0.52°). This varies slightly because the Moon's orbit is elliptical — at perigee it appears about 14% larger than at apogee, which is why 'supermoons' look marginally bigger. The Sun's angular diameter averages about 1,919 arcseconds, making total solar eclipses geometrically possible.
What is the difference between angular size and angular resolution?
Angular size is how large an object actually appears in the sky, while angular resolution is the smallest angular separation a telescope or eye can distinguish as two separate points. The human eye resolves about 1 arcminute; a 10 cm telescope resolves roughly 1.2 arcseconds. An object must be larger than the instrument's resolution limit to appear as a disk rather than a point of light. Most stars are so distant that even the largest telescopes see them as unresolved points despite their enormous physical size.
Why do planets look like disks through a telescope but stars do not?
Even the nearest stars are so extraordinarily far away that their angular diameters are measured in micro-arcseconds, far below the diffraction limit of any ground-based telescope. Planets in our Solar System, by contrast, range from a few to tens of arcseconds in angular size and are therefore resolvable as disks. Atmospheric seeing — the blurring caused by turbulence — limits ground-based resolution to roughly 0.5–2 arcseconds under typical conditions, which is why space telescopes like Hubble can image fine planetary detail unavailable from the ground.