How do I calculate actual aperture diameter and area from a 35mm-equivalent focal length?

Asked 10/13/2014

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If a camera has a 1.5× crop sensor and the lens is described as 50mm equivalent at f/2.8, how do I work out the actual aperture diameter and area? Should crop factor be applied to the aperture value, or only to the focal length? I'm asking about the physical aperture size, not equivalence for depth of field.

Originally by Idan Shechter. Source · Licensed CC BY-SA 4.0

Idan Shechter

11y ago

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The aperture size is a property of the lens only and does not depend on the crop factor. It does depend, however, on the actual focal length of the lens (not the "equivalent" focal length).

So you need to obtain the actual focal length by dividing by the crop factor.

$$f_\text{actual} = \frac{f_\text{equivalent}}{\text{crop factor}}$$

You can then calculate the size (diameter) of the aperture (strictly speaking the size of the entrance pupil, which is the image of the aperture) by dividing the focal length by the f-number N (which does not need to be divided by the crop factor).

$$\begin{align} \text{Aperture diameter} &= \frac{f_\text{actual}}{N} \\ &= \frac{f_\text{equivalent}}{N \times \text{crop factor}} \end{align}$$

So in your case the calculation is:

$$\begin{align} \text{Aperture diameter} &= \frac{50\,[\text{mm}]}{2.8 \times 1.5} \\ &= 11.9\,[\text{mm}] \end{align}$$

Originally by user1375. Source · Licensed CC BY-SA 4.0

user1375

11y ago

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Generated from our catalog & community — verify before relying on it.

Use the actual focal length, not the 35mm-equivalent focal length.

For a 1.5× crop camera:

  • actual focal length = 50mm ÷ 1.5 = 33.3mm
  • aperture diameter = focal length ÷ f-number = 33.3 ÷ 2.8 ≈ 11.9mm

So the aperture (more precisely, the entrance pupil diameter) is about 11.9mm.

To get area:

  • radius ≈ 11.9 ÷ 2 = 5.95mm
  • area = πr² ≈ 3.1416 × 5.95² ≈ 111mm²

Key point: do not multiply the f-number by crop factor when calculating physical aperture size. The f-number is a property of the lens and determines exposure the same way regardless of sensor size. Crop factor only changes the equivalent field of view, so you use it to recover the actual focal length from the equivalent one.

If you were comparing depth of field equivalence between formats, crop factor can matter there, but not for the physical aperture calculation itself.

UniqueBot

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11y ago

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