How to measure the AOV (Angle of View) and focal length of the lens (35mmfilm equivalent)  
130703  There are two ways to measure AOV. 1. Letter Paper  This method is easy to do but is accurate only for rectilinear lenses, not fisheye lenses. A rectilinear lens will record straight horizontal and vertical lines as straight lines. A fisheye lens will record some straight lines as curved lines. 2. Tape Measure  This method is accurate for both rectilinear and fisheye lenses. To measure Horizontal Angle Of View (HAOV) take a landscape photo or video of a horizontal tape measure from a measured distance (X). Make sure that the tape measure intersects the center of the image. Y becomes the width of the tape measure in the image. W and Z are equal, and are the image width in pixels. 130602  This AOV spreadsheet XLS file will do the calculations for you, no calculator required. Download it and open it with Excel or any XLS compatible spreadsheet program like Google Docs online spreadsheet. The 16:9 diagonal, horizontal and vertical AOV ratios are 1.15, 1, 0.526 The 4:3 diagonal, horizontal and vertical AOV ratios are 1.2, 1, 0.75 This is a procedure to measure the horizontal AOV (angle of view) of an 808 camera. You will take a video or photo of a standard piece of paper from a known distance. You will need a scientific calculator. The vertical angle of view and the diagonal angle of view are not measured here. For reference, a 35mm camera has a 36x24mm film image size. With a 50mm lens the camera has a diagonal, horizontal and vertical AOV of 47, 40 and 27 degrees, respectively. In 808 cameras, the AOV of a video frame and a photo frame can be different. You need to decide which one, or both, you want to measure. If a video frame, you need to take a short video of a paper sample, then use a software tool (like VirtualDub) to extract a frame to a JPG image, and then measure the pixels in the JPG image using a photo editor. If a photo frame, you will measure the pixels in a JPG image using a photo editor.
1 m = 1000 mm = 39.37 inch width of ANSI letter paper = 11 inch = 279 mm. width of ISO A4 paper = 11.7 inch = 297 mm. Sample test photo used to calculate AOV and focal length. 
Formula (I'm showing my work)  Math for my #3 camera  Math for my #1 Camera 
W = the horizontal width of the whole photo in pixels  1280 pixels  640 
X = the lens to paper distance in inches  36 inches  12 
Y = the paper width in inches  11 inches  4.906 
Z = the paper width in pixels, measured in a graphics editor  492 pixels  310 
K = Field of view inches = (WY) / Z  K = (1280*11) / 492 = 28.62 inches  
tan(AOV/2) = K/(2X)  
AOV = angle of view
degrees AOV = arctan(K/2X) * 2 AOV = arctan(WY/2XZ) * 2 
AOV = arctan(28.62 /
72) * 2 = 21.68 * 2 = 43.36 degrees 
AOV =
arctan((640*4.906)/(2*12*310)) *2 = 40.16 degrees 
The following formulas calculate the equivalent35mmfilm focal length from AOV. Math is from Bob Atkins.  
For a rectilinear lens. The frame size for 35mm film horizontal width is 36mm. frame size = 36.  
AOV = 2 * arctan(frame size / (focal length * 2))  
AOV / 2 = arctan(18 / equivalent35mmfilm focal length)  
tan(AOV)/2) = 18 / equivalent35mmfilm focal length  
Equivalent35mmfilm focal length = 18 / tan(AOV /2)  focal length = 18 /
tan(43.36 / 2) = 45.28mm 

To calculate equivalent35mmfilm focal length from W, X, Y and Z, the tan and arctan cancel out, resulting in this simple formula with no trigonometry.  
equivalent35mmfilm focal length = 18 / tan(arctan(WY/2XZ))  
equivalent35mmfilm focal length = 18 / (WY/2XZ)  
Equivalent35mmfilm
focal length = (36XZ) / (WY) 
equivalent35mmfilm focal length = (36 * 36 * 492) / (1280 * 11) = 45.28mm 