Angular Size Calculator (Apparent Size of the Moon, a Building, a Star)
How big an object looks, as an angle in degrees and arcminutes, from its real size and distance — or the real size from the angle it covers.
Results
Angular size in degrees
0.5178
°
Angular size in arcminutes
31.07
′
Angular size in arcseconds
1864
″
Size of an object that covers that angle
—
What this tool does
Angular size is the angle an object covers in your view: θ = 2 × atan(s ÷ 2d). For small angles this is close to s ÷ d radians, so 57.3 × s ÷ d gives degrees. The Moon is about 3,474 km across and 384,400 km away on average, so it covers roughly 0.52° (31 arcminutes) — almost exactly what the Sun covers, which is why total eclipses happen. As a rough guide, a fist at arm's length spans about 10° and a finger about 1°. Run it backwards to find the real size of something whose distance and apparent angle you know; use the same unit for size and distance.
Formula
θ = 2 × atan(s ÷ 2d) · s = 2 d × tan(θ ÷ 2)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
sz | Size of the object (any unit) | — |
dd | Distance to the object (same unit as the size) | — |
an | Angular size you know (degrees) | ° |
TD | Angular size in degrees | ° |
TM | Angular size in arcminutes | ′ |
TS | Angular size in arcseconds | ″ |
SZ | Size of an object that covers that angle | — |
Worked example
- Size of the object (any unit)3474
- Distance to the object (same unit as the size)384,400
- Angular size in degrees0.5178 °
- Angular size in arcminutes31.07 ′
- Angular size in arcseconds1864 ″
Limitations
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.