The angular size of Earth from Moon is 1.909 degrees, plus or minus 0.150 degrees. Angular or apparent sizes are frequently used in astronomy to calculate the apparent size of faraway objects.
The angular or apparent size is set upon the optics principle that the farther an object is, the smaller it appears. Apparent size does not calculate the actual object size. Rather, it calculates the object dimensions as it appears to a viewer. The process is not as difficult as it seems.
How to Calculate Angular Size
Note: this example will compute the apparent size of the Moon from the Earth. If you want to calculate the angular size of Earth from Moon, there are online angle calculators available.
You will need a calculator, metric tape measure and metric ruler. Grab the ruler and set at arm’s length. Get the object’s apparent size; use millimeters. In the case of the Moon, it will be around 5 to 8 millimeters. It will vary depending on your arm’s length and the tine of the year. Take down the measurement (S).
Get the metric tape to get the figures between your eye and the ruler you are holding at arm’s length. You may need an assistant to get the figure right. But you can get a good estimate by measuring your arm’s length from your shoulder to your thumb.
Take down the measurement (D). Divide S by D. The result is the object’s apparent size in radius. In this example, D = 760 mm and S = 7 mm. 7 mm / 760 mm would be 0.0092 radians.
How to Change Radius to Degrees
To make the conversion, the 1 radian = 57.3 degrees formula should be used. The result would be 0.0092 * 57.3 = 0.527 degrees.
The Moon has a lightly elliptical orbit. However, its distance can vary. At its farthest the Moon is 406,700 kilometers away. It is nearest at 356,400 kilometers. The nearest point is called the perigee; the farthest is known as the apogee. Because the perigee and apogee differ, the angular size of Earth from Moon can vary too.
This astronomical measurement is also known as an angular diameter. In astronomy, the measurement used is in arc-minutes. Here, one arc-min is equal to 160 of one degree. The apogee diameter is 29.87 arc-min while at perigee it is 33.89 arc-min. The average is 31.1 arc-min.