# How do you calculate the focal multiplier of a non-full frame camera?

I'm currently using a Sony RX100 Mark 3 camera and want to buy a Canon 6D + 24-105 F4 L lens from an online retailer, which is not in my country.

(before continuing I'd like to state that there are no camera retailers in my city which have a full-frame camera + this lens for testing so I can get a hands-on test and not ask this question)

I'm worried about the wide-range focal length of my camera as I want to buy a camera and a lens combination that will give me a wider angle of view as I intend to shoot more landscapes.

I am aware that the 6D is a full-frame camera, but I am just wondering if my Sony, which has a focal range of (8.8mm - 25.7mm, as written on the camera) has the exact same range of view at the wide end as a full frame + the before mentioned lens.

I have made some calculations and divided the size of the full-frame sensor (36mm x 24mm) to the size of my camera's sensor (13.2mm x 8.8mm) and came up with the focal multiplier for my camera (I'm not sure if this is how you calculate it, it's just a "gut feeling").

In the end, I came up with a 2.72x focal multiplier for my Sony camera and when I apply this to the focal range of my camera (8.8mm - 25.7mm) I get a equivalent of ~24mm x ~70mm.

Now, since this gives me approximately 24mm on the wide end, my assumption is that I should buy a lens with a wider focal length on the full frame setup, so going under 24mm.

Are my assumptions/calculations correct?

• 24mm "equivalent" is already quite wide...back in the days, a wideangle was usually a 28mm and remember that it's the ratio that counts: you have a 28/24 = 16% wider lens. Unless you want a "ultra" wide angle (not for landscapes, more for special effects), you will be fine. Use a focal length simulator online to preview the effect. From bobatkins.com/photography/technical/field_of_view.html you get 74° horizontal by 53° vertical field of view. It quite good for landscapes and more than that, stitching would be preferable anyway.
– FarO
Oct 13, 2015 at 10:06
• This is probably a good question in a general sense, but the easiest way to check the "equivalent" focal length range of a camera such as the RX100 is to just check the specs from Sony. They've already done the calculation. Oct 13, 2015 at 11:08
• You can find DOF/FOV apps on the web, to simulate the shot so you can get a feel for what the numbers mean. Oct 13, 2015 at 14:46
• This page says your camera has a 24mm-70mm equivalent focal length, so your calculations are bang on. Oct 13, 2015 at 18:09

Your calculation for the focal length multiplier is correct.

However you wont finder a wider "standard" zoom than 24mm, they tend to stop there as a matter of convention. So you will probably need a standard 24mm-x zoom and a wide angle zoom, of which Canon has a few models, covering the range 17mm-40mm, 16mm-35mm and 11mm-24mm. All of these will be significantly wider than your RX100 III.

• I'm not necessarily looking for a "standard" zoom and have searched around a bit since posting the question and it does seem that the 16-35mm would be a good lens, since it fits my budget and is "significantly" (I would say) wider than my Sony. Oct 13, 2015 at 9:16
• @RaduGheorghiu "fits my budget" on a US$1500 (new) lens is prompting my next remark, if you're purchasing used. You may want to check whether it's the Mk I or the Mk II version of the 16-35/2.8L. Oct 13, 2015 at 13:05 • @inkista I'm talking about the 16-35mm f4 which I've found for about US$1000, not the f2.8. But I will check your link. I was thinking that I don't need that extra stop when shooting landscape. Oct 13, 2015 at 13:08
• @RaduGheorghiu Ah. I keep forgetting newer lenses...Good choice! Oct 13, 2015 at 13:16
• @inkista No worries, I've been behind with "the times" too, up until recently when I decided to upgrade. Thank you for your link, it's very good and informative :-) Oct 13, 2015 at 13:17

How is the crop factor, sometimes called magnification calculated?

The size of image sensor or film, in the jargon of photography, is called the “format”. For every format there is a focal length that delivers what is called the “normal” perspective. By normal we are taking about a perspective that replicates human vision. A “normal” perspective is achieved when we mount a lens with a focal length that approximately matches the diagonal measure of the film or image sensor frame.

As an example; the full frame (Fx) format measures 24mm height by 36mm length. The diagonal of this rectangle measures 43.27mm. If we mount a lens with this focal length the resulting image replicates the “human perspective”.

Technically the angle of such a lash-up view will be about 45⁰, camera is held in the horizontal (landscape) position.

Now the camera industry rounds the “normal” focal length for the 35mm full frame up to 50mm. This tradition started about 100 years ago with the introduction of the first 35mm, the Leica.

If a 50mm is considered “normal” for the Fx, what is wide-angle and what is telephoto?

As a rule of thumb a lens 70% of normal or shorter falls in the realm of wide-angle. Thus 50 x 0.7 = 35mm.

A lens 35mm or shorter is considered wide-angle for the Fx.

Telephoto is 200% or longer. Thus 50 x 2 = 100mm or longer is the realm of telephoto for the Fx.

Now your Sony sports a miniature sensor. The Sony’s imaging chip measures 8.8mm height by 13.2mm length. The diagonal measure of this format is 16mm. How can we compare lenses between these two different frame sizes (Full frame vs. your camera)? We divide diagonals and the result is a crop or magnification factor. Correct is 43.27 / 16 = 2.7. This is the crop factor of your Sony.

What is the value of this number? Old gray hairs like me (77 years old) know the full frame and its lenses as to their angle of view. If you have never used a full frame than the only value will be -- you have lots of used but good lenses for the full frame on your shelf and you want to use them. Otherwise -- not much value. I think.

How do we use this crop factor? Mount a 50mm lens on the Sony RX100 and the 50mm projects an image of the Sony’s smaller sensor. The smaller sensor can only see the center area of image presented by this lash-up. How will the Sony RX100 preform with a 50mm. The view will be 50mm x 2.7= 135mm. In other words if you mount a 135mm lens on a Fx, the view delivered will be about the same as a 50mm mounted on the Sony RX100. This is because the smaller sensor of the Sony RX100 can only view the central portion of the 50mm lens. The peripheral of the image formed by the 50mm is lopped off (cropped).

How do we figure “normal” perspective? If we stand before a glass window and gaze at a vista, we can trace the outlies of objects on the glass with wax pencil. Such a drawing is made to the natural or “human” perspective. Can we duplicate this human perspective with the camera? Yes if we follow these rules.

1. The camera replaces the human eye as to distance to the glass window.
2. An image is taken (focal length not a factor).
3. A contact print is made from this image.
4. The image is viewed from a distance equal to the focal length of the camera lens. The image matches the “human perspective”
5. The image is enlarged and viewed from a distance. A lens used about equal to the diagonal of the format. Most photographs are viewed from a distance about equal to the diagonal measure of the pictures dimension. The math as to what lens delivers a “normal” view, takes into account the degree of enlargement and the viewing distance

Today’s miniature cameras make a tiny image that is nearly useless unless magnified. We shoot with a full frame with a 50mm; we make an 8x12. The magnification applied is about 8X. The diagonal of the 8x12 is 14 inches (350mm. We tend to view from this distance.

If we make a 16 x24 from a full frame and a 50mm lens is used: This large print will likely be viewed from about 40 inches, (the diagonal). The magnification to make is about 20x; 50mm x 20 = 1000mm or about a meter (about 40 inches). The image is seen to have a “normal perspective.

We are taking a rule-of-thumb and not a law engraved in stone. Most images are viewed as OK even if the we violate this rule of thumb. An exception is the portrait. Too short or too long a lens and the image violates this rule and people say I don’t photograph well. The portrait is best when the lens used is about 2x thru 2.5x the focal length. Such a combination presents an image naturally viewed from a distance that replicates the human perspective.

• Thank you for your post, Alan. But, can you please format it a bit, for readability? Thank you! Oct 13, 2015 at 14:07
• "Lens used is about 2x thru 2.5x the focal length" what? Oct 13, 2015 at 14:43
• Art has no rules but as a rule of thumb, portraiture sells better and wins contest if the focal length is 2 thru 2 ½ times the “normal”. The normal is a lens a lens the equal of the diagonal of the frame. For the full frame the format is 24mm by 36mm and the customary “normal” is 50mm. Thus the lens of choice is 100mm thru 125mm. Such a lash-up delivers a perspective that has low distortion. The 105mm has been applauded. This method takes into account the degree of enlargement and the viewing distance for a finished print or display. For the compact digital, 30mm is “normal” thus 60 thru 90mm. Oct 13, 2015 at 19:50