# Specialized Calculators for Crop Factorand Equivalent Focal Length relationships

## The Numbers of Crop Factor

Other pages here, Part 1 and Part 2 explain Crop Factor and Equivalent Focal Length in detail, but this page provides four calculators for it.

Two Equivalent Fields of View: If two cameras with two sensor sizes of Full Frame 1x and 1.6x crop factors (fill in your own number for the 1.6x) then:

• If standing in the same place, the 1x crop factor could use a focal length 1.6x longer (for example, 160 mm vs 100 mm) to then see the same smaller field of view as the 1.6x crop factor sees. The 1.6x longer focal length is the conventional Equivalent Focal Length placed on the 1x camera, as compared to the lens focal length that the 1.6x crop factor is using.
• Or, if both cameras use the same lens focal length, the 1x camera can stand 1.6x closer (meaning at distance / 1.6, as compared to the distance of the 1.6x crop, for example 10 feet vs 16 feet) to see the same smaller field of view. In the same similar way, this could be called an Equivalent Distance needed to see the same field of view as the 1.6x camera.

Sensor Size and Crop Factor and Aspect Ratio are important numbers for calculations, such as Field of View or Depth of Field. It is not always easy to determine those exact numbers, but maybe these calculators can help. And another page might help about Sensor Size.

## Calculate Crop Factor from Sensor Size

Crop Factor = Diagonal dimension of 35 mm film
Diagonal dimension of THIS camera sensor

### 1. Calculate Crop Factor

1 Known Sensor Dimensions:

Sensor Width  mm

Sensor Height mm

2 Sensor Type:

b

If you know accurate sensor size (width × height in mm), then use it here. Other tries sometimes are approximations. And published specs are rounded in some degree (including focal length, crop factor, aspect ratio and sensor dimensions), losing a slight bit of the exact precision of calculation. Also the 4th calculator just below is another method to determine crop factor.

Crop Factor is about the sensor size, comparing it to 35 mm film size as the standard comparison. If this division computes the Crop Factor to be 1.5x, it means that the 35 mm film frame dimensions are 1.5x larger (the area is about 2.2x larger, varying slightly with aspect ratios). This size is compared numerically measured on the diagonals to account for different shape sensors. If 3:2 aspect, a 1.5x crop frame is 1/1.5 or 2/3 the dimensions of the 35 mm film. The diagonal of 35 mm film is known to be 43.26661 mm, and which is considered to be crop factor 1x. Sensor size crops the Field of View captured, and Crop Factor compares it to the Field of View that Full Frame or 35 mm film frames would see.

## Calculate Sensor Size from Crop Factor

### 2. Calculate Sensor Dimensions

Crop Factor and

Max Image Size, pixels
Width x Height

or Aspect Ratio

The 2nd calculator is the reverse, calculating sensor size from crop factor and Aspect Ratio. Aspect Ratio is about the Shape, simply width / height of the sensor mm or the image pixels. The most common aspect ratios in cameras today are 3:2 = 1.5:1 in DSLR, 4:3 = 1.333:1 in compacts and phones, and 16:9 = 1.778 for video, in camcorders and HDTV. The publicized aspect ratio is often rounded Nominal numbers, which is pretty close, but you can instead enter the exact pixel dimensions of the images straight out of the camera and it will be calculated either way.

Our camera specifications might not tell the Crop Factor or the sensor dimensions. However we are often told its Equivalent focal length relationship to a comparison lens for 35 mm film, which can then tell us crop factor. And since crop factor describes sensor size, we can compute sensor dimensions from it, using the 4th calculator below about using Equivalent Focal Length.

## Calculate Equivalent Focal Length

Equivalent Focal Length for 35 mm film (1x) =  Crop Factor  ×  Focal Length of lens on THIS camera

### 3. Calculate Equivalent Focal Length

Actual real Focal Length mm on
a Crop Factor x sensor

Equivalent focal length is conventionally compared to be used on 35 mm film size, which is called full frame (1x crop).

Also x,  x and x crops

The Focal Length of our lens is simply always what it says it is (zoom of course changes it to what zoom says it is.) The focal length choice is selected for the sensor size, but the physical lens cannot be modified by the sensor size present. A 50 mm f/1.8 lens on a full frame body is still the same 50 mm f/1.8 if on any smaller cropped body. However the Field of View depends on both the focal length and the sensor size.

The Equivalent Focal Length applies to a different lens on a different camera sensor because the term conventionally applies to another lens used on 35 mm film frame size, Full Frame (1x crop) that would give the same Field of View on that camera sensor as THIS lens on THIS camera sensor (assuming both are standing in the same place). But the term can be used regarding another different camera NOT a 1x crop frame.

The math can be reversed to compute the lens for THIS camera that would compare to the Full Frame view, or to some other sensor size view, but unless that is stated, convention of Equivalence Focal Length is about a lens used on a Full Frame sensor. For example, see the camera specification in the next calculator section where it is clearly shown as referring to 35 mm film size.

Equivalent Focal Length simply means "Sees same Field of View" if the Equivalent lens is used on a Full Frame camera. You may or may not have any interest in what a full frame sensor might see (users with 35 mm film experience likely will). 35 mm film size is called a 1x crop factor. The Field of View W×H dimensions vary with aspect ratio, but "same Field of View" here means the image diagonal is the same dimension (the lens image circle is the same size.)

Using this 3rd calculator for Equivalent Focal Length, you can:

• Compute equivalent focal length that would show the same Field of View compared on a standard 1x full frame sensor (1x the default comparison, which is the standard universal usage). So a 1x crop sensor is always included here, specified or not.
• Can reverse the crop factors (place 1x at the TOP ↑ of the calculator, and the larger crop factor at ANY OR ALL of the ADDED CROPS (all entered will be shown) to show equivalence used on this sensor relative to a focal length used on a 1x full frame sensor, if entered that reversed way.
• Compare equivalent focal lengths for Equivalent Field of View of any two crop factors. Shows all ADDED sensors relative to the TOP ↑ sensor.
This general case is Equivalence = focal length × (crop1 / Equiv_crop2), with the focal length used on the crop1 numerator sensor, and the Equivalent Focal Length used on the Equiv_crop2 denominator sensor. Unless stated otherwise, standard convention compares to 35 mm film frame size called Full Frame size, 1x crop factor in the denominator.

The initial page default shows examples of what can be expected.

## Compute Crop Factor and Sensor Dimensions from Equivalent Focal Length

Equivalent Focal Length is computed from Crop Factor, and Crop Factor and Sensor Size can be reverse computed from (accurate) Equivalent Focal Length.

Crop Factor = Equivalent focal length on 35 mm film (1x)
Focal length of lens on THIS camera

### 4. Calculate Crop Factor andSensor Dimensions fromEquivalent Focal Length

THIS Focal Length mm

35 mm Equiv FL mm

Aspect

Equivalent focal length is often the only sensor size specification given on small cameras (sensor dimensions and crop factor are often not mentioned). These two numbers (Focal Length used in current picture, and Effective Focal Length for 35 mm film cameras) are often shown in each images Exif data (see more detailed info). Except compacts that zoom may not show it in Exif, but they should show Effective Focal Length directly in the lens specs (in manual or in product advertising), this way:

For example, the specification for some compact camera's zoom lens might say:

Focal Length: 4.5 - 81.0 mm (35 mm film equivalent: 25 - 450 mm)

This is the manufacturers data, and the lens specification should be shown on the camera manufacturers web site product page, in most product advertising, in your camera manual, and often in the image Exif data. So what it says is that this zoom lens focal length is 4.5 to 81.0 mm.

This was a Canon Powershot compact. It says its 4.5 mm lens sees the equivalent view of a 25 mm lens on a 35 mm film camera (the tiny compact sensor has to use the short lens to fill its small frame with the same Field of View that the larger 35 mm film would see).

It also says that a 35 mm film camera would see the same Field of View if that camera used a 25-450 mm lens. This is the convention normally used, that the Equivalent Focal Length is used on the Full Frame camera to see an equivalent Field of View on it. The Equivalence is Not used on this camera, which uses its own lens. All of these numbers are rounded, but it should be pretty close. If you have 35 mm film experience, this may be meaningful to you, to tell you what to expect that this camera is going to do.

So simple division can compute crop factor to be (25 mm / 4.5 mm), or (450 mm / 81 mm), Both of which compute the same 5.556x crop factor. This is the actual size relationship of the two digital sensors (diagonals), which affects the Field of View that can be captured from the lens. And since 35 mm film size is well known, then with the correct aspect ratio, crop factor can also be used to compute sensor dimensions. However these published values (crop factor, sensor size, aspect ratio, even focal length) are often rounded, stated as slightly less precise values than they actually are. Be sure to specify Aspect Ratio properly for your camera.

## Macro Lens Reproduction Ratio on Cropped Sensor

The Crop Factor simply does not affect the lens reproduction ratio. A 1:1 lens is 1:1 on any sensor, but 1:1 speaks of the magnified object size, NOT necessarily the frame size. Crop factor certainly affects the size of the frame containing the image (the Field of View), so it does affect later enlargement of that frame, but not the initial magnification of objects within the frame (it does not affect reproduction ratio).

1:1 is a fixed reproduction ratio, which is 1:1 object size on any sensor size (even if the magnified object size won't fit on a smaller sensor). Since any lens remains unchanged by any sensor size, its reproduction ratio is also unchanged, and the focus distance where 1:1 occurs is unchanged. A smaller sensor will simply and necessarily crop the overall Field of View, but the lens magnification remains the same.

What 1:1 means is if photographing a ruler with a lens at 1:1, then a sensor width of 24 mm will show a field width of 24 mm. At 1:1, a sensor width of 36 mm will show a field width of 36 mm. The meaning of 1:1 is that one mm actual will be one mm size on any sensor size. The overall Field of View does change with sensor size. A smaller sensor does crop the image frame smaller, but at 1:1, subject objects within any frame size will be the same 1:1 real life size in the image (same magnification).

Reproduction ratio is (actual real object size in mm) / (object image size in mm). Full size ratio is 1:1. Half size ratio is 2:1.

Magnification is the reciprocal, (object image size in mm) / (actual real object size in mm). Full size magnification is 1x. Half size magnification is 0.5x.

A 1:1 reproduction ratio normally increases the required exposure +2 EV. However (at least for Nikon) the modern macro lens reports the new adjusted f/stop, to agree with an not-through-the-lens meter. Then 1:1 may not show exactly 2.0 EV because modern lenses use internal focusing which can shorten focal length, in which case are probably about 1/3 EV or 1/2 EV less than 2 EV.

## Extension Tube Magnification on Cropped Sensors

Again, the Crop Factor simply does not affect the lens reproduction ratio. A 1:1 lens is 1:1 on any sensor, but 1:1 speaks of the magnified object size, NOT necessarily the frame size.

Macro lenses are more expensive, but are vastly more easy and versatile and convenient (meaning usable) than extension tubes, which are fixed length without any versatility, which can be a bit much for a beginner (read up well first). Or instead a bellows does provide extension versatility. Either extension tubes or bellows might lose camera automation, like lens stop down or auto exposure.

Or Macro lenses likely will include the automation, and they focus normally and easily, from infinity to typically 1:1, very easy to use, even at 1:1, you simply just focus like any other lens (depth of field at 1:1 is virtually zero, so you will want to use at least f/16 at 1:1, and a speedlight flash helps both light and motion shake). The macro lens is the best choice by far, except for price.

An extension tube is an empty tube (with no glass elements) mounted between camera body and lens, to extend the lens forward to focus closer for greater magnification. It loses the ability to still focus at infinity. Normal lenses on extension tubes (if near 1:1) really don't change focus much, instead we focus by moving the camera back and forth a couple of inches to find the one place it is in focus, at whatever ratio the extension does. If you want a different size view, you have to change the extension tube length (a different or multiple tubes).

Extension tubes add much more magnification to shorter lenses than to longer lenses. Adding a 20 mm extension tube to a 200 mm lens is 10%, but it is double on a 20 mm lens. And double is necessary to achieve 1:1.

Again, Crop Factor is not a factor of reproduction ratio, although it does affect overall Field of View size (a smaller sensor crops the image smaller).
Saying, with a 1:1 lens on a cropped sensor, the subject is still the same size at 1:1 (same magnification), but the overall frame is cropped smaller.

There is also a calculator that covers all of this for the purpose of copying slides (with macro lens or extension tube). The Extension Tube Formulas have been moved there too.

## Teleconverters on Cropped Sensor

These add-on lens adapters (behind the lens) contain optical glass elements which enlarge the size of the image projected by the lens, which then is a longer new effective focal length of the combination. A teleconverter is NOT for macro, instead it zooms focal length more on distant scenes, but it loses the closest focus ability. The teleconverter might be named 1.4x magnification for example, however there are also some wide angle adapters, perhaps 0.7x for example (more commonly for wider view in telescopes).
• Teleconverter, for example marked 1.4x (this is √2, which is 1.414).

The effective focal length of the combination becomes 1.4 times the lens focal length. 100 mm becomes 141 mm.
The crop factor of the combination becomes previous crop factor x 1.414. Crop factor 1.5 becomes 2.1x.
A 1.4x converter reduces the Field of View by 1/1.4, to be 0.7x previous width.
A 1.4x converter increases the lens aperture numbers (reduces light transmission) by one EV.

• Wide angle converters, for example 0.7x (this is 1/√2, which is 0.707).

The effective focal length of the combination becomes 0.7x the lens focal length. 100 mm becomes 70.7 mm.
The crop factor of the combination becomes previous crop factor x 0.7. Crop factor 2 becomes 1.4x.
A 0.7x converter increases the Field of View by 1/0.7, to be 1.41x previous width.
A 0.7x converter reduces the lens aperture numbers (increases light transmission) by one EV.

The f/stop formula is:  f/stop number = focal length / aperture diameter.
If focal length becomes 1.4x longer, then f/stop number (of same diameter) becomes 1.4x greater.
A f/stop Number 1.4x greater is one EV, 2x greater is 2 EV.
The focal length causes this f/stop change, Not the crop factor.