Calculating the required focal length

[phkc0704081]

Is there a table or a calculation where I can calculate the focal length to exactly a subject at a known size at a known distance away?

For example, if I have a subject that is 40 meters long and I will be 1.06 km away from it, what focal length do I need, on a Full Frame camera, to exactly fit my entire subject?

If this can be done on the Photopills App, even better. thanks

 

[wfooshee]

All I can come up with is trigonometry. Divide the length by twice the distance: L/2D. Take the arctangent of that. arctan(L/2D). That's the apparent viewing angle of half of the object (the angle at the end of a right triangle whose base is your line of sight,) so multiply by two. Now you have the viewing angle of the object, but in radians. Multiply by 180 and divide by pi to get degrees. Now that you have the angle of view the object uses, you can look at the table here to find an appropriate focal length.

 

[AlanKlein108 24]

if I have a subject that is 40 meters long and I will be 1.06 km away from it, what focal length do I need, on a Full Frame camera, to exactly fit my entire subject?

Gemini said​

To calculate the required focal length to fit a subject perfectly into your frame, you can use the basic lens formula based on the relationship between the sensor size, subject size, and distance.

For a Full Frame camera (36mm×24mm sensor), if you want the 40-meter subject to fit across the long edge (horizontal) of the frame:

The Formula​

f=Od×s
Where:

• f = Focal Length
• d = Distance to subject (1.06 km=1,060,000 mm)
• s = Sensor size (36 mm for the long edge of Full Frame)
• O = Object/Subject size (40 meters=40,000 mm)

The Calculation​

f=40,000 mm1,060,000 mm×36 mm
f=40,00038,160,000
f=954 mm

---

Summary of Results​

• To fit the 40m subject horizontally: You need a 954mm lens.
• To fit the 40m subject vertically: You would use the 24mm sensor height in the formula, resulting in a 636mm lens.

Since 954mm is a very specific and long focal length, you would likely use an 800mm lens (which would leave some "breathing room" around the subject) or a 600mm lens with a 1.4x or 2.0x teleconverter.

Doing this in PhotoPills​

If you want to use the PhotoPills app mentioned in your shared forum post:

1. Open the "Field of View" (FoV) tool.
2. Select your camera model (to set the Full Frame sensor size).
3. Switch the "Input" mode to "Distance and Subject Size" if available, or simply toggle the Focal Length until the "Horizontal FoV" at your specific distance (1.06 km) equals 40 m.