Image size in millimeters is approximated by multiplying the sensor size in inches by 16. The circle of confusion is 1/500 of the image size for standard definition and 1/1000 for high definition video. The depth of field is then calculated using the equations given by KerryG.
Rather than implement a lookup table of common image sensor sizes, the computations used here estimate the diagonal measurement of the image in millimeters by multiplying the sensor size by 16. This gives exact results for 1", 1/2" sensors and results to within 2% for many consumer camcorders. Note, however, this approximation underestimates by 11% the image captured by a 1/3" sized sensor.
Another way to obtain the size of the captured image is by multiplying 43.3 by the actual focal length and then dividing by the equivalent 35mm focal length. The equivalent 35mm focal length may be reported by the manufacturer or measured experimentally. For more information see how to calculate 35mm equivalent focal length by George Kroonder.