Depth of Field Calculator

Depth of field is the band of object distances whose blur circle on the sensor stays smaller than the circle of confusion, the largest defocus disc a viewer still reads as a point. Everything in the calculation flows from the hyperfocal distance H, equal to the focal length squared divided by the product of the f-number and the circle of confusion, plus the focal length. The near limit is s(H - f) divided by (H + s - 2f) and the far limit is s(H - f) divided by (H - s), which goes to infinity once the subject distance reaches H. Focal length enters squared, so doubling from 50mm to 100mm quarters the depth of field at a fixed aperture and distance, while the f-number enters linearly. The circle of confusion is a viewing convention, not a property of the camera. The values of 0.029mm for full frame, 0.019mm for APS-C, 0.015mm for Micro Four Thirds, 0.043mm for medium format and about 0.006mm for a phone sensor all derive from one rule: roughly 1/1500 of the sensor diagonal, which corresponds to an 8 by 10 inch print viewed at 25cm. Print larger or inspect at 100 percent and the working CoC should shrink, narrowing the calculated depth of field. The equations are also paraxial thin-lens approximations that drift at macro distances or with asymmetric pupils, and stopping down past roughly f/11 on full frame trades geometric depth for diffraction as the Airy disc grows with the f-number.

Depth of field was a working concern from the earliest days of photography, when slow plates forced long exposures and photographers needed to know how much of a scene a given stop would hold. Rigorous treatment came with the German optical industry: Moritz von Rohr at Carl Zeiss in Jena published theoretical work on photographic objectives from 1899 onward, and the convention of tying the acceptable blur circle to a fraction of the negative diagonal is generally credited to Zeiss practice. English-language derivations of the near and far limit equations appear in physics texts of the period, including Louis Derr's Photography for Students of Physics and Chemistry of 1906. By the 1930s the results were engraved on hardware. Lens barrels carried depth-of-field scales, paired f-number marks flanking the focus index, so a photographer could read the sharp range off the barrel without arithmetic. In 1932 the f/64 Group formed in California around Ansel Adams, Edward Weston and Imogen Cunningham, taking its name from the smallest aperture on a view camera and making front-to-back sharpness an aesthetic programme. The conventions were later challenged from within: Harold Merklinger argued in The Ins and Outs of Focus in 1992 that the standard circle-of-confusion approach misjudges distant detail. Digital multiplied the sensor formats needing their own CoC, and since about 2016 smartphones have simulated shallow depth of field computationally rather than optically.