How this calculator works
A lens brings one plane into perfect focus, and points nearer and farther than that form small circles on the sensor. Up to a chosen circle of confusion the eye still reads those circles as sharp. The conventional limit is the sensor diagonal divided by 1500, about 0.029 mm for full frame, which corresponds to a point just under 0.2 mm on an 8 by 10 inch print seen from a comfortable distance. Using that limit, the hyperfocal distance is the focus distance beyond which everything from half the hyperfocal distance to infinity is acceptably sharp. For a closer subject, the near and far limits bracket the focus distance; as the focus distance reaches the hyperfocal distance, the far limit runs to infinity and the depth becomes unbounded.
Formula
circle of confusion c = sensor diagonal / 1500. hyperfocal distance H = f^2 / (N x c) + f, with f and c in the same units. near limit = H x s / (H + (s - f)). far limit = H x s / (H - (s - f)). depth of field = far limit - near limit. Here s is the focus distance and N the f-number.
Worked example
A 50 mm lens at f/8 focused at 5 metres on a full-frame sensor has a circle of confusion of 43.267 / 1500 = 0.02884 mm. The hyperfocal distance is 0.05 squared / (8 x 0.00002884) + 0.05 = 10.88 metres. The near limit is 10.88 x 5 / (10.88 + 4.95) = 3.44 metres and the far limit is 10.88 x 5 / (10.88 - 4.95) = 9.17 metres, so the depth of field is 5.73 metres. Focusing instead at the hyperfocal distance of 10.88 metres would make everything from 5.44 metres to infinity sharp.
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Frequently asked questions
What is the circle of confusion and why fix it?
It is the largest blur spot that still looks like a point in the final picture. The diagonal divided by 1500 is a long-standing convention for prints viewed at a normal distance; larger prints or closer viewing need a smaller limit and therefore less depth of field.
Why is the depth not symmetrical around the focus point?
The far limit moves faster than the near limit as you approach the hyperfocal distance, so the sharp range always extends further behind the subject than in front. At one third of the hyperfocal distance the split is roughly one third in front and two thirds behind.
Does sensor size change depth of field?
For the same framing and aperture, a smaller sensor gives more depth because the focal length needed is shorter. If you compare at the same focal length and distance instead, the smaller sensor simply crops and the depth looks similar.
Why is there no far limit in my result?
At or beyond the hyperfocal distance every distance to infinity is acceptably sharp, so the far limit is infinite and cannot be shown as a finite number. The page reports the range as running to infinity instead.