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On my Nikon D3000, how do I figure the focal length equivalence? In other words, if I want a lens that is just like a 50mm lens on a 35mm film SLR, I need to multiply by a factor. What is the factor, and how is it derived?

Also, when I buy a new lens for it, and the box says 70mm-300mm, I assume that's the true focal length of the camera and not the equivalent, so I have to apply the factor. Is that correct?

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Some reference questions you can read. What is the difference between focal length and crop factor? photo.stackexchange.com/questions/139/… What is “angle of view” in photography? photo.stackexchange.com/questions/5917/… –  Vian Esterhuizen Dec 8 '11 at 17:25

6 Answers 6

up vote 7 down vote accepted

What is the factor, and how is it derived?

The factor (also commonly called a 'crop factor') is a measurement of how much larger a full-frame image sensor is than the sensor in your camera. People say the D3000's crop factor is 1.5 because a full-frame sensor is 1.5x larger than the D3000 sensor.

A full-frame sensor is 36mm x 24 mm. The sensor in the Nikon D3000 is 23.6mm x 15.8mm.

Comparing the sensor sizes along each dimension:

36mm / 23.6mm = 1.52 (approximately)

24mm / 15.8mm = 1.52 (approximately)

You can see how the full-frame sensor is around 1.5x the size of the D3000 sensor, hence the 1.5x crop factor.

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The focal length is a property of the lens and not the camera. Thus, a 50mm lens is a 50mm lens, no matter what body it is attached to. What does change is the Field of View (FoV) of the lens-body combination. The smaller the sensor, the smaller the FoV for a given focal length.

Attaching a lens with a certain FL on a full-frame (35mm) camera gives a certain FoV. Attaching the same lens on a body with smaller sensor gives a FoV which is smaller by the same factor. This is called the crop-factor, or multiplier. The net effect is the same as of attaching a a lens of longer FL (by the same factor) on a full frame camera.

So, for Nikon APS-C cameras, the crop factor is 1.5. It means that a 100mm lens on an APS-C body produces the same FoV as a 150mm lens on a full frame body.

When you buy a lens of 70-300mm FL, it is 70-300 on every body you attach it. But the effect on D3000 would be as if it was 1.5 longer on a D3.

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Read this for a good definition of Crop Factor and what it exactly means. It will also give you a better understanding of the question you're asking.

The Crop Factor of the Nikon DX series is 1.5. This means you would multiply your 70 mm by 1.5 to get a new field of view, equivalent to that of a 105 mm lens.

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For a Nikon, the multiplication factor for their APS-C 'DX' crop sensors is 1.5. Therefore, the closest you can get to a 50mm lens would be a 35mm... (35 x 1.5 = 52.5mm)

When you buy lenses they are stated with their full and proper focal length on a Full Frame camera (FX Digital or 35mm Film). So take whatever length the lens is sold as and multiply by 1.5. For example - the lens 70-300mm you state above becomes 105-450mm equivalent on a DX crop sensor body.

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Just to point out that actually the focal length doesn't change, a full frame sensor is like watching a picture on a 40" TV, now take that picture (at exactly the same pixel dimensions and put it on a 37" TV and you will be missing the edges, that is essentially what is happening, you are stripping the edges off of the picture you are taking.

Below is an example:

enter image description here

You can see the full frame image is larger and the APS-C is smaller, the focal length hasn't changed, it just appears that it has.

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And, to follow the analogy, also generally "sits closer" so that the red area fills as much of your view as the bigger screen from further back. (Printing or viewing the final image at a similar size.) –  mattdm Dec 9 '11 at 15:23

You multiply by 1.5222.

There is a good explanation of crop factors at http://www.kenrockwell.com/nikon/dx.htm

and the actually number for the D3000 can be found at http://www.kenrockwell.com/nikon/d3000.htm

So you 70-300 would act like a 106-456mm lens.

And to get a 50mm equivalent, you divide by 1.522, so you need a 33mm lens.

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I'm curious, why the down vote? –  Paul Cezanne Dec 12 '11 at 0:19

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