How the Angular Size Calculator works
Angular size explains why physically different objects can look equally large in the sky. It connects physical size and distance to the angle seen by an observer. The core relationship used here is Exact angular diameter = 2 × atan(size ÷ (2 × distance)). For small angles, angle in radians ≈ size ÷ distance. If you are building a complete observing or imaging setup, use the Field of View Calculator alongside this page rather than treating one number in isolation.
Worked example and interpretation
The Moon is about 3474 km across and roughly 384,400 km away on average, producing an apparent diameter close to half a degree.
For broader physical context, the NASA/JPL Solar System Dynamics is a useful external reference.
When this calculator is useful
Use it for planets, moons, nebulae, galaxies, spacecraft or any target where a physical size and distance are known.
When the result involves angular size, field, observing conditions or a current target, continue with Distance Converter. For a different but related perspective, Light Travel Time Calculator can connect the formula to an actual observing, telescope or Solar System context.
Diagrams
Assumptions, accuracy and practical limits
The result assumes the entered physical size is the projected diameter and the distance is measured consistently to the same target. Irregular shapes and large-angle geometry need extra care.
A second external cross-check is available from NASA Moon. Not for operational or published work.
Reference table: apparent sizes of familiar objects
| Object | Degrees | Arcseconds |
|---|---|---|
| Moon (mean distance) | 0.5178° | 1,864.2″ |
| Sun (1 AU) | 0.5334° | 1,920.2″ |
| Jupiter at opposition (4.2 AU) | 0.0128° | 45.9″ |
| ISS (420 km altitude, 109 m wide, overhead) | 0.0149° | 53.5″ |
The Sun and Moon are almost the same apparent size, which is why total eclipses are possible; the ISS overhead appears around a minute of arc across, too small to resolve by eye.
Related SpaceTracker.live tools
Continue with Field of View Calculator, Distance Converter and Light Travel Time Calculator.
Worked scenarios: sizes you can picture
A US quarter is 24.26 mm across. Held at 2.68 m from your eye, it covers the same angle as the Moon (about 0.52°), so it just blocks out the Moon.
Jupiter, about 139,820 km wide, subtends roughly 46″ at 4.2 AU. A person 1.8 m tall would span one arcsecond at a distance of about 371 km. At 100× magnification, the Moon’s 0.52° appears like an object about 52° wide, which is why it overfills the field of an eyepiece.
Common mistakes and reference sizes
- Confusing diameter and radius. The formula uses the full diameter unless you double the radius.
- Mixing units. The size and the distance must use the same unit before you divide.
- Reading arcminutes as degrees. One degree is 60 arcminutes, and one arcminute is 60 arcseconds.
| Object | Angular size |
|---|---|
| Sun | about 31.6′–32.7′ |
| Full Moon | about 29.4′–33.5′ |
| Venus | 10″ – 66″ |
| Jupiter | 30″ – 50″ |
| Mars | 3.5″ – 25″ |
| ISS overhead (109 m at 400 km) | about 56″ |
| Pea at arm’s length (7 mm at 70 cm) | about 0.6° |
More questions answered
Why does the Moon look larger near the horizon?
It is an illusion: the angular size is the same, but the brain compares it with landscape features. Measure it with your fist at arm’s length (10°) or your thumb nail (about 1.5°) to confirm.
Is angular size the same as apparent brightness?
No. Angular size describes how wide an object appears, while apparent magnitude describes how bright it appears.
Frequently asked questions
Why do the Moon and Sun look the same size?
The Sun is about 400 times wider but also about 400 times farther away, so both subtend roughly half a degree.
Can I use the small-angle formula instead?
For angles below a few degrees the approximation size ÷ distance (in radians) is accurate to a tiny fraction; the calculator uses the exact tangent form.
Do distance units matter?
Only that diameter and distance use the same unit; the ratio is what sets the angle.