Effectively, a crop sensor camera does the following transformations:

f_crop,eff = f_crop,real * C

N_crop,eff = N_crop,real * C

ISO_crop,eff = ISO_crop,real * C²

where f is the focal length and N is the aperture number. These transformations, when applied, give the (1) same field of view, (2) same depth of field, (3) same background blur, (4) same noise given equivalent sensor technology, (5) same exposure.

An example: you have a Canon crop sensor (1.6x crop) camera with 50mm f/1.2 lens are are shooting at ISO 100. Effectively, the lens is a 80mm f/1.92 lens and you are effectively shooting at ISO 256. So, to take an equivalent picture using a full frame camera, you need to find a 80mm f/1.92 lens (closest you will find is 85mm f/1.8 lens), and shoot at ISO 256 (closes you will find is probably ISO 250).

What some people forget is the transformation to aperture. For example, if you have a 17-55mm f/2.8 crop zoom, you cannot claim it's equivalent to 24-70mm f/2.8 full frame zoom. The focal lengths are close enough: 17-55mm is equivalent to 27.2-88mm, but the aperture is equivalent to f/4.48! So the f/2.8 crop zoom is more like a f/4 full frame zoom.

If you forget to transform the aperture, you are forgetting two things:

• Equivalent depth of field and background blur: a full frame camera will have shallower depth of field and more background blur at the same aperture number. But, if you transform the aperture as well, you are getting equivalent DoF and background blur.
• A full frame sensor can be used with 1.6² = 2.56 times the ISO sensitivity at the same noise level, because the sensor area is 2.56 times bigger.

To remind you of the importance of the aperture, think in the following way: if you have a 50mm f/1.2 lens, and make the sensor very tiny (8x crop), do you have 400mm-equivalent f/1.2-equivalent lens? Of course not, as even 400mm f/2.8 is huge, costing over $10000! You have 400mm-equivalent f/9.6-equivalent lens then.

So, to answer your question: yes, a crop sensor camera effectively multiplies the focal length with the crop factor. But, at the same time, it multiplies the aperture too with the crop factor.

Effectively, a crop sensor camera does the following transformations:

f_crop,eff = f_crop,real * C

N_crop,eff = N_crop,real * C

ISO_crop,eff = ISO_crop,real * C²

where f is the focal length and N is the aperture number. These transformations, when applied, give the (1) same field of view, (2) same depth of field, (3) same background blur, (4) same noise given equivalent sensor technology, (5) same exposure.

An example: you have a Canon crop sensor (1.6x crop) camera with 50mm f/1.2 lens are are shooting at ISO 100. Effectively, the lens is a 80mm f/1.92 lens and you are effectively shooting at ISO 256. So, to take an equivalent picture using a full frame camera, you need to find a 80mm f/1.92 lens (closest you will find is 85mm f/1.8 lens), and shoot at ISO 256 (closes you will find is probably ISO 250).

What some people forget is the transformation to aperture. For example, if you have a 17-55mm f/2.8 crop zoom, you cannot claim it's equivalent to 24-70mm f/2.8 full frame zoom. The focal lengths are close enough: 17-55mm is equivalent to 27.2-88mm, but the aperture is equivalent to f/4.48! So the f/2.8 crop zoom is more like a f/4 full frame zoom.

If you forget to transform the aperture, you are forgetting two things:

• Equivalent depth of field and background blur: a full frame camera will have shallower depth of field and more background blur at the same aperture number. But, if you transform the aperture as well, you are getting equivalent DoF and background blur.
• A full frame sensor can be used with 1.6² = 2.56 times the ISO sensitivity at the same noise level, because the sensor area is 2.56 times bigger.

To remind you of the importance of the aperture, think in the following way: if you have a 50mm f/1.2 lens, and make the sensor very tiny (8x crop), do you have 400mm-equivalent f/1.2-equivalent lens? Of course not, as even 400mm f/2.8 is huge, costing over $10000! You have 400mm-equivalent f/9.6-equivalent lens then.

So, to answer your question: yes, a crop sensor camera effectively multiplies the focal length with the crop factor. But, at the same time, it multiplies the aperture too with the crop factor.

Effectively, a crop sensor camera does the following transformations:

f_crop,eff = f_crop,real * C

N_crop,eff = N_crop,real * C

ISO_crop,eff = ISO_crop,real * C²

where f is the focal length and N is the aperture number.

An example: you have a Canon crop sensor (1.6x crop) camera with 50mm f/1.2 lens are are shooting at ISO 100. Effectively, the lens is a 80mm f/1.92 lens and you are effectively shooting at ISO 256. So, to take an equivalent picture using a full frame camera, you need to find a 80mm f/1.92 lens (closest you will find is 85mm f/1.8 lens), and shoot at ISO 256 (closes you will find is probably ISO 250).

What some people forget is the transformation to aperture. For example, if you have a 17-55mm f/2.8 crop zoom, you cannot claim it's equivalent to 24-70mm f/2.8 full frame zoom. The focal lengths are close enough: 17-55mm is equivalent to 27.2-88mm, but the aperture is equivalent to f/4.48! So the f/2.8 crop zoom is more like a f/4 full frame zoom.

If you forget to transform the aperture, you are forgetting two things:

• Equivalent depth of field and background blur: a full frame camera will have shallower depth of field and more background blur at the same aperture number. But, if you transform the aperture as well, you are getting equivalent DoF and background blur.
• A full frame sensor can be used with 1.6² = 2.56 times the ISO sensitivity at the same noise level, because the sensor area is 2.56 times bigger.

To remind you of the importance of the aperture, think in the following way: if you have a 50mm f/1.2 lens, and make the sensor very tiny (8x crop), do you have 400mm-equivalent f/1.2-equivalent lens? Of course not, as even 400mm f/2.8 is huge, costing over $10000! You have 400mm-equivalent f/9.6-equivalent lens then.

So, to answer your question: yes, a crop sensor camera effectively multiplies the focal length with the crop factor. But, at the same time, it multiplies the aperture too with the crop factor.

Effectively, a crop sensor camera does the following transformations:

f_crop,eff = f_crop,real * C

N_crop,eff = N_crop,real * C

ISO_crop,eff = ISO_crop,real * C²

where f is the focal length and N is the aperture number. These transformations, when applied, give the (1) same field of view, (2) same depth of field, (3) same background blur, (4) same noise given equivalent sensor technology, (5) same exposure.

An example: you have a Canon crop sensor (1.6x crop) camera with 50mm f/1.2 lens are are shooting at ISO 100. Effectively, the lens is a 80mm f/1.92 lens and you are effectively shooting at ISO 256. So, to take an equivalent picture using a full frame camera, you need to find a 80mm f/1.92 lens (closest you will find is 85mm f/1.8 lens), and shoot at ISO 256 (closes you will find is probably ISO 250).

What some people forget is the transformation to aperture. For example, if you have a 17-55mm f/2.8 crop zoom, you cannot claim it's equivalent to 24-70mm f/2.8 full frame zoom. The focal lengths are close enough: 17-55mm is equivalent to 27.2-88mm, but the aperture is equivalent to f/4.48! So the f/2.8 crop zoom is more like a f/4 full frame zoom.

If you forget to transform the aperture, you are forgetting two things:

• Equivalent depth of field and background blur: a full frame camera will have shallower depth of field and more background blur at the same aperture number. But, if you transform the aperture as well, you are getting equivalent DoF and background blur.
• A full frame sensor can be used with 1.6² = 2.56 times the ISO sensitivity at the same noise level, because the sensor area is 2.56 times bigger.

To remind you of the importance of the aperture, think in the following way: if you have a 50mm f/1.2 lens, and make the sensor very tiny (8x crop), do you have 400mm-equivalent f/1.2-equivalent lens? Of course not, as even 400mm f/2.8 is huge, costing over $10000! You have 400mm-equivalent f/9.6-equivalent lens then.

So, to answer your question: yes, a crop sensor camera effectively multiplies the focal length with the crop factor. But, at the same time, it multiplies the aperture too with the crop factor.