#### Amin Sabet

##### Administrator Emeritus

- Jul 3, 2010

- 124

As time goes on, we have more and more formats to compare. For example, Fuji brought back 2/3" format with the X10, and the RX100 uses a 1" sensor, while the Canon S100 uses a 1/1.7" sensor and the Panasonic LX7 in 4:3 aspect ratio effectively uses a 1/1.8" sensor. Expressing focal length and relative aperture in terms of 135 format equivalents is very useful for comparing angle of view and depth of field possibilities across formats and gives a rough estimate of how well these systems will compare for handheld, low light photography if using similar sensor technology.

The purpose of this post is to provide an easy method to calculate things like 135 format equivalent focal length and relative aperture using only the sensor dimensions, the information marked on the lens itself, and Google.

**If you are not interested in doing such calculations, then definitely skip the rest of this post!**

In order to calculate equivalent focal lengths and equivalent relative apertures, we need to know the crop factor for each format.

**Crop factor can be defined in either of the following two ways**:

1) Crop factor = the ratio of the

**diagonal**dimensions of the respective formats

2) Crop factor = the square root of the ratio of the

**areas**of the respective formats.

The above two definitions/methods will give the same results when calculating the crop factor for a format with a 3:2 aspect ratio but will differ when calculating for a format with an aspect ratio other than 3:2. For example, 4/3 has a 2.00X crop factor based on the ratio of diagonal format dimensions and a 1.96X crop factor based on the root of the sensor area ratio.

Many of you realize that Google has a very convenient built-in calculator. For example, if you search for "2+2", the first search result will be "4". Below are a series of calculations which can be plugged directly into Google search* for deriving useful relationships between formats.

*It should be noted that the ISO-standard for math notation says that "lg(x)" denotes the 10-logarithm of x, rather than the 2-logarithm. Google does it differently, by taking lg(x) as the 2-logarithm of x. The equations below will work for their intended purpose (doing calculations in Google), but mathematically they don't use commonly accepted notation.

The following are a series of calculations based on the ratio of the diagonal dimensions of the two formats and are written in a form which can be copied directly to Google:

**Crop factor**, where

**SW**=sensor height (mm);

**SH**=sensor width (mm):

(sqrt((36^2)+(24^2)))/(sqrt((

**SW**^2)+(

**SH**^2)))

**Difference in stops between two formats**, where

**SW1**=sensor 1 width (mm);

**SH1**=sensor 1 height (mm),

**SW2**=sensor 2 width (mm);

**SH2**=sensor 2 height (mm):

2*lg((sqrt((

**SW1**^2)+(

**SH1**^2)))/(sqrt((

**SW2**^2)+(

**SH2**^2))))

**135 format equivalent focal length**, where

**SW**=sensor height (mm);

**SH**=sensor width (mm);

**FL**=focal length:

((sqrt((36^2)+(24^2)))/(sqrt((

**SW**^2)+(

**SH**^2))))*

**FL**

**135 format equivalent relative aperture**(equivalent f-number), where

**SW**=sensor height (mm);

**SH**=sensor width (mm);

**RA**=relative aperture (f-number):

((sqrt((36^2)+(24^2)))/(sqrt((

**SW**^2)+(

**SH**^2))))*

**RA**

The following are a series of calculations based on the square root of the ratio of the areas of the two formats and are written in a form which can be copied directly to Google:

**Crop factor**, where

**SW**=sensor height (mm);

**SH**=sensor width (mm):

sqrt((36*24)/(

**SW***

**SH**))

**Difference in stops between two formats**, where

**SW1**=sensor 1 width (mm);

**SH1**=sensor 1 height (mm),

**SW2**=sensor 2 width (mm);

**SH2**=sensor 2 height (mm):

2*lg(sqrt((

**SW1***

**SH1**)/(

**SW2***

**SH2**)))

**135 format equivalent focal length**, where

**SW**=sensor height (mm);

**SH**=sensor width (mm);

**FL**=focal length:

(sqrt((36*24)/(

**SW***

**SH**)))*

**FL**

**135 format equivalent relative aperture**(equivalent f-number), where

**SW**=sensor height (mm);

**SH**=sensor width (mm);

**RA**=relative aperture (f-number):

(sqrt((36*24)/(

**SW***

**SH**)))*

**RA**

Using the above calculations in Google, it's easy to derive the following table

Here are a few additional Googleable calculations which may be useful:

**Number of stops separating two f-numbers**for a given format, where

**RA1**=f-number 1;

**RA2**=f-number 2:

2*lg(

**RA1**/

**RA2**)

**F-number**which is

**X**stops

**than another given f-number (**

*slower***RA**):

((sqrt(2))^(

**X**)))*

**RA**

**F-number**which is

**X**stops

**than another given f-number (**

*faster***RA**):

((sqrt(2))^(

**-X**)))*

**RA**

Special thanks to everyone in this thread (especially GideonW) for double checking my math and offering ways to improve this resource.