When you read about 35mm format cameras and lenses, you may understand the basic concept of field of view vs the focal length of your lens.

In a general sense, it’s commonly stated that the longer the focal length of your lens, the narrower the image zone (field of view) will be. Use a shorter focal length lens and it makes your image wider. The point is, it’s normally stated that you are either getting more narrow or wider with your field of view depending on the focal length of your lens.

The question I’ve sometimes been asked by students and workshop attendees is “how wide? how narrow?” My answer is typically “well there’s a formula for that.” At which point the conversation usually ends because I don’t remember the formula and it goes beyond the scope of what we are doing at the moment, however, it’s a valid question and one that is better explained offline from working in the field.

So, here’s the trigonometric formula for making that calculation.

Angle of view (in degrees) = 2 ArcTan( sensor width / (2 X focal length)) * (180/π)

Using a calculator, you would use radians. If using degrees, you drop the (180/π) part of the formula.

For a full frame (35mm) camera this assumes a sensor width of approximately 35mm.

For practical purposes, I don’t normally keep a trigonometric calculator with me in my camera kit, so I have a little cheat sheet I’ve created. The truth is, I don’t normally keep a cheat sheet with me either but have instead memorized the focal lengths angular fields of view. I know that a 50mm lens will give me around 40 degrees of angular field of view, which is easy to estimate with my eyes and hands. I know that an 18 mm lens will give me roughly 90 degrees of angular field of view. I also know that 200mm lens will give me roughly a 10-degree field of view and that my 500mm lens will give me roughly a 4-degree field of view. These aren’t precise, but by memorizing the main focal lengths I can get a rough idea of which lens I want to use to make a shot based on a quick estimate of how “wide” the scene is in from of me. Since I use zoom lenses most of the time, it’s fairly simple to figure out which lens I want to use on a particular scene by roughly estimating the angular field of view I wish to capture.

So, what about APS-C crop sensor field of view?  It’s fairly simple. Just multiply the lens focal lengthy by either 1.5 (Nikon/Sony) or 1.6 (Canon) to calculate the effective focal length of that lens on your crop sensor body and then use the cheat sheet to calculate your rough angular field of view. For example, assume I’m using a 100mm lens on a Nikon D500 (crop sensor body), 100mm x 1.5 = 150 mm. The field of view for a 150mm lens will be approximately 13.7 degrees. Easy as pie.

Here’s the cheat table for estimating actual angular field of view based on a 35mm (full frame) sensor.

Focal Length     Angular Field of View
11mm                        117.1 degrees
14mm                        104.3 degrees
16mm                          96.7 degrees
24mm                          73.7 degrees
35mm                          54.4 degrees
50mm                          39.6 degrees
85mm                          23.9 degrees
100mm                        20.4 degrees
150mm                        13.7 degrees
200mm                        10.3 degrees
300mm                          6.9 degrees
400mm                          5.2 degrees
500mm                          4.1 degrees
600mm                          3.4 degrees
800mm                          2.6 degrees
1000mm                        2.1 degrees

You can read more about this in greater detail on the Nikonians website at this link.