Photography Formulae

A small collection of useful formulae (formulas) for the photographer, including a couple of handy calculators.

A DSLR and a scientific calculator tightly lit in black and white.
A DSLR and a scientific calculator tightly lit in black and white.

Hyperfocal Distance

Hyperfocal distance (H) defined as the distance at which a lens must be focused for everything beyond half that distance (H/2) to be in acceptable focus. This is especially useful since it is the distance at which maximum depth of field is achieved. This is where most fixed focus cameras (eg. smartphones) will be focused at and also the ideal point for many photographs; think basic landscape focus distance. The form below can be used to calculate H for various systems, circle of confusion is provided here by a drop down box allowing you to select your system format:

Focal Length (mm)
Aperture (f-number)
Circle of Confusion (mm)
Hyperfocal Distance (m)
H = metres

The form above uses the formula H = F squared / f * c  ;  where F is focal length, f is f-number and c is circle of confusion.

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Depth of Field

The depth of field is the distance between the nearest & furthest points that are in acceptable focus. For situations where the distance to the focused upon object (d) is significantly larger than the lens focal length (F) (i.e. most non macro photography), the depth of field can be derived from the Hyperfocal distance (H). The form below can be used to do this:

Hyperfocal Distance (m)
Object Distance (m)
Depth of Field (m)
DoF = metres

The form calculates both furthest & nearest points of focus and then takes their difference. Furthest acceptable focus point = H * d / H – d  ;  nearest acceptable focus point = H * d / H + d.

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Circle of Confusion

A concept that oft lives up to its name by causing much confusion. Strictly speaking a camera image is only in perfect focus at the plane of focus, the distance from which the light is brought to a perfect point of focus on the camera sensor. In reality there is a larger workable depth of focus that we will perceive as acceptable. As we gradually move away from the focal plane, light is focused on the sensor as tiny circles, not points; these tiny circles build up the picture that we see. How large can the circles get whilst we still perceive the focus to be acceptable – the diameter of that circle is the circle of confusion measurement. This is somewhat subjective and has many variables, such as viewer’s eyesight, camera sensor size, size of displayed / printed image, distance from which image is viewed. For a more detailed consideration of these factors, see Canon’s webpage or the Wikipedia page for even more detail. Below, is a simplified table giving some example values that are typical of those used in these calculations:

Camera Sensor FormatCircle of Confusion (mm)
4/3 system0.015
APS-C - x1.6 crop0.018
APS-H - x1.3 crop0.023
35mm0.030
645 medium format0.047
Example circle of confusion measurements for different camera systems.

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