A little help with calculating...

[themos]

If you are given a FOV rating for binoculars as x meters at 1000 meters and you are wondering what's that in degrees, go here and click on Radius & Chord, next to Radius put in 1000 and next to Chord put the other number x, hit Calculate and read off Central Angle

So, 114 -> 6.5353 degrees

Cheers!

[mhc]

The approximating forumla is:

Angular size (degrees) = 57 x ^height / _distance

So, 114m at 1000m gives:

57 x ¹¹⁴/₁₀₀₀ = 6.498 degrees

57 is used to convert radians to degrees. The actual value should be ¹⁸⁰/_PI ~57.30 (2 decimal places).

[themos]

Ah, but you chopped off 180/3.1415926 at 2 significant figures. If we work with 3 (as our data, 114, has 3 significant figures), we must use 57.3

and then 57.3 * 114 / 1000 = 6.53 to 3 significant figures.

Your approximate formula cannot be used for large angles. For instance, a value of 1000 would give 57 degrees (or 57.3) instead of the correct 60.

At the small angle we are considering it's only off by milli-degrees.

[mhc]

Ah, but you chopped off 180/3.1415926 at 2 significant figures. If we work with 3 (as our data, 114, has 3 significant figures), we must use 57.3

and then 57.3 * 114 / 1000 = 6.53 to 3 significant figures.

Themos, the first line of my post says:

The approximating forumla is:

Got that from my newly received OU Introducing Astronomy text book (Short Course S194).

The last line says:

The actual value should be ¹⁸⁰/_PI ~57.30 (2 decimal places).

I did that bit myself

In conclusion,