Crop Factor Calculator (full-frame equivalent)

Understanding the crop factor calculator — concept and principle

Lenses are usually described by what they would show on a full-frame (36 × 24 mm) camera. On a smaller sensor the same lens shows a narrower view and, at the same framing, gives deeper depth of field. This calculator multiplies a lens's focal length and f-number by your sensor's crop factor to give the full-frame equivalent field of view and depth-of-field aperture, while showing that the exposure aperture stays the same.

How it is calculated

• Crop factor c = 43.27 mm ÷ sensor diagonal (preset values such as 1.5 for most APS-C, 1.6 for Canon APS-C, 2.0 for Micro Four Thirds).
• Equivalent focal length = focal length × c.
• Equivalent aperture for depth of field = f-number × c.
• Exposure aperture = the f-number you set, unchanged.

The principle

The angle of view depends on the ratio of sensor size to focal length. Shrinking the sensor by a factor c is like cropping the center of the full-frame image, which is the view a lens c times longer would give on full frame. Depth of field depends on the physical size of the aperture opening (focal length ÷ f-number) and on how much the image is enlarged for viewing; to match a full-frame shot with the same framing and aperture diameter, the f-number must also be multiplied by c. Exposure, however, depends on light per unit of sensor area, which is set by the f-number alone, so f/1.8 is f/1.8 for shutter speed and ISO on any format.

Worked example

Default: 35 mm lens at f/1.8 on APS-C (1.5×).

1. Equivalent focal length: 35 × 1.5 = 52.5 mm.
2. Depth-of-field equivalent aperture: 1.8 × 1.5 = f/2.7.
3. Exposure aperture: f/1.8 (unchanged).

So this lens frames like a 52.5 mm "normal" lens on full frame, with background blur similar to a full-frame lens at about f/2.7.

How to read the result

Use the equivalent focal length to choose lenses for a purpose: around 24–35 mm equivalent for wide scenes, 50 mm for a natural view and 85–135 mm for portraits. Use the equivalent aperture to predict background blur and, roughly, total light gathered from the scene, which affects noise when comparing formats at the same shutter speed. A larger crop factor makes very shallow depth of field harder and long telephoto reach easier.

Common mistakes

• Thinking the lens itself changes; a 35 mm lens is always 35 mm, only the view changes.
• Raising ISO or shutter speed because of the "equivalent f/2.7"; exposure still uses f/1.8.
• Using 1.5 for every APS-C body; Canon APS-C is about 1.6.
• Applying the crop factor to a lens's minimum focus distance or physical size.

FAQ

Frequently asked questions

What does a 35 mm lens equal on APS-C?

About 52.5 mm on full frame with a 1.5× crop, or 56 mm on Canon's 1.6×.

Does a crop sensor make my lens brighter or darker?

No; the exposure at f/1.8 is the same on any sensor.

What is the crop factor of a smartphone main camera?

Often between about 2.7 and 7, depending on the sensor size.

Sources: Sidney F. Ray, Applied Photographic Optics, Focal Press