Everyone knows a long lens gives shallow depth of field. It is not quite true, and the way it is untrue is worth knowing. Depth of field falls off hard with focal length at a fixed distance — but if you change lenses and then walk until the subject is the same size in the frame, almost all of that difference vanishes.
At 24 mm you stand a metre away and get 293 mm of depth of field. At 200 mm you stand eight and a half metres away and get 287 mm. An eight-fold change of focal length moves the depth of field by two per cent.
What actually changes is the background: the long lens magnifies it enormously, so the out-of-focus area is far more blurred even though the in-focus slab is the same thickness. That is what people are seeing when they say a long lens has less depth of field — and that is the part the aperture diameter governs, because a 200 mm at f/2.8 is a 71 mm hole against a 24 mm lens's 8.6 mm.
The sharp slab itself is a different quantity. At constant framing it is set by the f-number and the format, and the focal length cancels out of the arithmetic almost exactly. Put a 200 mm at f/11.2 next to a 50 mm at f/2.8 — identical 17.9 mm holes — and the long lens has four times the depth of field. Same hole, four times the depth: it was never the hole.
Depth of field grows as you stop down, without limit. Sharpness does not. Light passing a small aperture spreads, and the blur it makes — the Airy disc — grows in direct proportion to the f-number: 2.44 × wavelength × N. Somewhere the diffraction blur gets bigger than the circle of confusion you were willing to accept, and from there on every stop buys depth of field by spending resolution you cannot get back.
On the standard print criterion, diffraction reaches the circle of confusion at about f/21 on full frame, f/14 on APS-C, f/11 on Micro Four Thirds and f/8 on a one-inch sensor. Smaller sensors hit the wall sooner, for exactly the same reason they have more depth of field in the first place: everything is scaled down except the wavelength of light.
A decision, not a measurement. It is the largest blur circle you are prepared to call a point, and the traditional figure is the sensor diagonal divided by 1500 — which works out as roughly what an unaided eye resolves on a 10×8 print at arm's length. Every depth of field number anywhere depends on it, which is why two calculators can disagree and both be right. Switch the standard here to see how much it moves.
It maximises the range that is acceptably sharp, from half the hyperfocal distance to infinity — but it puts infinity right at the edge of acceptable, which means distant mountains are exactly as soft as you said you would tolerate and no sharper. If the far detail is the subject, focus on it instead and accept a nearer near limit. Landscape photographers who focus a third of the way in are using a rougher version of the same idea.
Because it genuinely does. The far limit is u(H−f)/(H−u), and as the subject distance u climbs towards the hyperfocal distance H the denominator goes to zero. One small step closer to H and the far limit leaps from a few tens of metres to unbounded. It is a real feature of the geometry, not a rounding artefact — and it is why hyperfocal focusing feels like a trick.
A thin lens in air, focused by moving the whole lens, with the subject distance measured to the lens rather than the sensor plane. Real lenses are thick, many focus internally, and their focal length changes as they focus — focus breathing — so close-up numbers drift from reality first.
That the only blurs are defocus and diffraction. Lens aberrations, which improve as you stop down, are not modelled, so the true optimum aperture on a real lens is usually a stop or so tighter than the pure diffraction crossover suggests. Sensor resolution and the anti-aliasing filter are absent too.
A wavelength of 550 nm for the Airy disc, green light at the eye's peak sensitivity. Red diffracts more and blue less, so a real image goes soft in the red channel first.
The depth-of-field limits are the classic thin-lens ones and are exact within that model —
no small-angle shortcuts. Verified in dof_model.py.
Near the subject the near and far limits sit almost equally either side (where “a third in front, two thirds behind” comes from, and even that only at moderate distances). Approach the hyperfocal distance and the far limit runs away to infinity while the near limit barely moves.
Everything scales down together (sensor, focal length for the same view, circle of confusion) except the wavelength of light. So the geometry gives you more depth of field and the physics takes it back at a wider aperture: a phone camera reaches its diffraction limit around f/3.
f/2.8 on a 50 mm lens is an 18 mm hole; f/2.8 on a 200 mm is a 71 mm hole. It governs the background: the long lens magnifies it, so the out-of-focus area is far more blurred though the sharp slab is the same thickness. It becomes the invariant when you compare formats.
At the same subject size in the frame, depth of field is set by the f-number and the format; the focal length very nearly cancels. A head-and-shoulders shot at f/2.8 on full frame gives 293 mm of depth of field at 24 mm from a metre away and 287 mm at 200 mm from eight and a half metres: an eightfold change of lens for a two per cent change. A 200 mm at f/11.2 has the same 17.9 mm hole as a 50 mm at f/2.8 and gives four times the depth of field. Matching the look on a smaller sensor needs the f-number divided by the crop factor, and since the focal length divides too, the hole comes out the same.
Most lenses change focal length slightly as they focus, and many internally focusing lenses change it a lot: a “70–200” can behave like a 140 at its closest distance. Every calculator assumes the marked focal length, so the closer you work, the more the arithmetic drifts from the lens in your hand.
This page has changed in 89 archived releases, but each of those was a site-wide pass, so none is attributable to this tool on its own and none is listed here. That is not a claim that the tool never changed — a release that reworked many pages at once may well have altered this one too. The changelog has them.