# How to calculate height of camera and ground coverage via geometry?

I have a GoPro7 that I will mount on a pickup vehicle to capture ground images with video capture.

The camera isn't top down but has about 20 (or 30) degrees inclination from the vertical axis. I want to capture the road that is 4m in width.

Other givens would be:

• Vertical Field of View: 71.0deg
• Horizontal FoV: 86.7deg
• Diagonal FoV: 100deg
• Sensor size: 1/2.3” (6.17×4.55mm)
• Aperture: f/2.8
• Zoom: 0%
• Frame width: 4:3

I would like to know if it is possible (and how) to calculate the needed height of the GoPro for this.

• The bottom of the frame will be narrower than the top of the frame because it is closer to you. Do you want to capture the 4m road at the bottom of the frame, the middle, or the top? Can the camera be turned toward the center of the road or must it face straight ahead? If straight ahead, how much of the 4m is left of centerline? The easiest way is to mark some spots on the road with chalk and move the camera until you can see what you want. Yes, it is quite possible if you describe exactly what you want. Feb 5, 2021 at 16:15
• Don't you remember SOHCAHTOA from high school trigonometry? Feb 5, 2021 at 17:26
• – scottbb
Feb 5, 2021 at 21:02
• What does this have to do with photography? Feb 5, 2021 at 23:13
• @Jonas, I don't want to sound like a grump, but I don't think it's an interesting question. It's a basic trigonometry question that I would have expected to solve easily in high school. There is simply 2 triangles involved, a few measurements given, and the unknowns easily calculable using the formulae that I linked to earlier. Feb 6, 2021 at 22:02

I will make a bunch of assumptions along the way along the lines of my comment. If I guess wrong, I hope you can adapt the calculation. Let us assume the camera is pivoted to the left so the 4m you want to see is equally split across the centerline of the frame. I will also assume the 4m is across the middle of the frame vertically. If the height of the camera is H the point on the ground will be H/tan(20) ahead of you. The half width of the frame is 2m, so you want 2=(H/tan(20))*tan(86.7/2), which gives H=0.77 meters or about 30 inches.

• thanks. but i was wondering if the sensor size, aperture, FoV, and magnification has something to add here Feb 7, 2021 at 6:25
• It is all about field of view. That sets the area you can see. The rest doesn't matter for that. Feb 7, 2021 at 14:57
• why does 0.77*tan(20) * tan(86.7/2) gives me negative? Feb 12, 2021 at 6:47
• Your calculator is probably set to radians instead of degrees. I used degrees because you gave the data that way. Check tan(45) If you are in degrees you will get 1 Feb 12, 2021 at 14:22