What is the hyperfocal distance formula, and how is it derived?

Hyperfocal distance is H = f² / (N × c) + f, where f is the lens's real focal length, N is the f-number, and c is the sensor's circle of confusion — the maximum acceptable blur-disc size the whole calculation is built around. Focus at H and everything from H/2 out to infinity reads as acceptably sharp.

What Each Term Actually Does

The f² term is why hyperfocal distance grows so fast with focal length — doubling the focal length roughly quadruples this term, which is why a 50mm lens's hyperfocal distance dwarfs a 24mm lens's at the same aperture, far more than a simple doubling would suggest. N sits in the denominator, so a narrower aperture (higher f-number) shortens the hyperfocal distance, extending the range of acceptable sharpness closer to the camera. c also sits in the denominator: a smaller circle of confusion (a stricter sharpness standard, typical of smaller sensors) makes the hyperfocal distance longer, not shorter, at a fixed real focal length and aperture — a detail that trips up more photographers than any other part of this formula, since a smaller sensor's overall reputation for 'more forgiving' depth of field actually comes from needing a shorter real focal length to match a given shot, not from the circle-of-confusion term alone.

Where the '+f' Comes From

The trailing +f term is a small correction that matters most at short hyperfocal distances (wide lenses, small apertures) and becomes negligible at longer ones — some simplified online calculators drop it entirely, producing a slightly different, usually shorter, result than the full formula. It comes from the thin-lens geometry relating image distance to object distance, not from an approximation or rounding choice.

See this formula applied to your own real numbers in the DoF & Hyperfocal Calculator, or read the full reasoning in the depth-of-field guide.