The hyperfocal calculation is a special case of the depth of field calculation. The benchmark is the capacity of an observer to perceive the image as in sharp focus or not. The calculations are subjective because they call for knowing the operation of the observer’s eye brain.
The bases: What is the allowable size of the circles of confusion on the final displayed image? The industry standard is: The diameter of the circle of confusion should be about equal to f 1/1000 of the viewing distance. If followed, the circles will appear as dimensionless points to the average observer. If the image is viewed at the typical reading distance of 200mm (20 inches), the maximum circle size is 500 ÷ 1000 = 0.50mm.
Now the modern camera sports a small image imaging sensor so we must magnify this image to get a useful displayed image size. Suppose a full frame (24mm by 36mm) camera is tasked to make an 8x10 image. The camera’s image must be enlarged 8 ½ X to stretch it to the 8x10 size. To achieve a sharp enlarged image, the circle of confusion, at the image plane must tolerate the enlargement. At the image plane it should be 0.50 ÷ 8.5 = 0.06mm or smaller.
Now the industry cannot predict the degree of magnification that will be required. The adopted rule-of-thumb is the a circle size of 1/1000 of the focal length. This method takes into account the generalization of focal length and magnification. For critical work Leica uses 1/1500 and Kodak used 1/1750. If a 50mm lens is mounted, using 1/1000 rule-of-thumb, the diameter of the circle of confusion at the image plane is 0.05mm. Using the Leica standard = 0.0333mm. Using the Kodak standard = 0.0286.
Let’s see if the 1/1000 rule works for an 8x10 made from an Fx format. To make the 8x10 display we enlarge 8 ½ X. Suppose we mount a 50mm lens, this sets the goal of the circle size at the image plane of 50 ÷ 1000 = 0.05mm. These will be enlarged 8 ½ times. The circle size on the final display is 0.05 X 8.5 = 0.4250mm. If viewed from standard reading distance, the criterion is 0.5mm. Our 8x10 sports a circle size of 0.425mm. We win and the image is perceived as being in sharp focus.
One more point: Video and cinema have reduced requirements because they present a moving image so it is more difficult for the eye brain to make the sharpness vs. non-sharp determination.
By the way, calculating the hyperfocal distance is easy.
Formula: All values in the same unit I choose millimeters
A 30mm lens set to f/8
D (working diameter of lens) = F ÷ f-number
D = 30 ÷ 8 = 3.75mm
H = hyperfocal distance
C = diameter circle of confusion
H = (F x D) ÷ C
Find hyperfocal distance using circle size 0.019mm
H = (30 x 3.75) ÷ 0.019
H = 112,55 ÷ 0.019
H= 5921mm = 5.9 meters = 20 feet.