Crop factor

Learning goal

You will be able to explain why the same lens gives a different frame on cameras with different sensor sizes, and read a lens correctly for your own camera. You will know roughly how big full-frame, APS-C and Micro Four Thirds sensors are and their crop factors; you will show that a small sensor changes not the focal length but only the angle of view; you will tell apart that the f-number stays the same on every sensor in terms of exposure, but depth of field changes for the same frame; you will explain with the image circle which sensors lenses fit; and you will choose the right distance for a portrait, on every skin, according to sensor size.

The question

Two friends stand side by side in a coppersmiths' bazaar. The same 50-millimeter lens is on both their cameras. From the same place, they photograph a coppersmith beating a pot at their bench. In one friend's frame, the coppersmith's whole bench, the hanging pots and the shop's door can be seen; in the other's frame, there are only the coppersmith's face, shoulders and the hands holding the hammer.

Is 50mm 50mm on every camera? The same lens, the same number, the same place; but a different frame. In this lesson we will talk about where this difference comes from, sensor sizes, the crop factor, and what this multiplier changes and what it doesn't.

Context

In Lesson 10.8, when calculating the safe shutter speed, we saw that on a small sensor you need to enlarge the focal length by a multiplier, and called it the crop factor. In the frames of the fisher on the pier, too, the angles given by 24, 50 and 200 millimeters were calculated for a full-frame sensor. This lesson focuses on the multiplier itself and clears up a common confusion: the crop factor doesn't change the lens; it only changes how big a piece of the lens's image the sensor takes.

This confusion has practical consequences. Whether a lens suits portraits, whether a second-hand lens fits your camera, what a photographer means on your camera when they say "85 millimeters"; all of these depend on reading this multiplier correctly.

Simple explanation

What are sensor sizes and the crop factor?

Cameras have a few common sensor sizes. A full-frame sensor is the same size as a 35-millimeter film frame: about 36 millimeters by 24 millimeters, with a diagonal of about 43 millimeters. The sides of the sensors called APS-C are about two-thirds that length, and their diagonals vary around 27 to 28 millimeters depending on the manufacturer. Micro Four Thirds sensors are smaller; their diagonals are about half of full frame.

The crop factor is the ratio of the full-frame sensor's diagonal to a sensor's diagonal. On APS-C this ratio is about 1.5, with some manufacturers about 1.6; on Micro Four Thirds it is about 2. Phone sensors are smaller still, and that is why phone cameras' focal lengths are usually given as full-frame equivalents. This multiplier is the key to calculating which full-frame focal length gives the same angle of view as a lens on that sensor, that is, the equivalent field of view.

Does the focal length change, or the angle of view?

A lens's focal length is a physical property coming from the structure of its glass, and it stays the same whatever body it is put on. A 50-millimeter lens is 50 millimeters on an APS-C body too. What changes is how much of the image the lens produces the sensor catches. The lens casts a round image behind it onto the sensor; a full-frame sensor takes a big rectangle of this image, while an APS-C sensor takes a smaller rectangle from its middle. The result is a frame similar to the angle of view a 75-millimeter lens would give on full frame.

The f-number doesn't change in terms of exposure either. An f/2 lens sends light of the same intensity to every point of the sensor on an APS-C body too; in the same scene, with the same shutter speed and the same ISO, it gives the same exposure. What changes is depth of field: to build the same frame on a small sensor you use a shorter focal length or a greater distance, and this deepens the slice of sharpness. Roughly, a portrait taken at 50 millimeters f/2 on APS-C is close, in depth of field, to a frame taken on full frame at 75 millimeters with an aperture around f/3.

Which lens fits which body?

The round lit area a lens casts behind it onto the sensor is called the image circle. The image circle of lenses designed for full frame is big enough to cover a full-frame sensor to its corners; these lenses also work without trouble on an APS-C body with the same mount, and the sensor only takes the middle. That is why many photographers who start with an APS-C camera choose full-frame lenses, thinking of the chance of moving to full frame later. Between different mounts, an adapter can also be used in some systems; an adapter doesn't change the focal length or the crop factor, but autofocus and aperture control may not work equally smoothly with every combination.

The reverse isn't always true. The image circle of a lens designed for APS-C is smaller; in systems where it can be put on a full-frame body, the corners of the frame go dark, or the camera switches to a crop mode by itself and records only the middle. When buying a second-hand lens, it matters for this reason to check which sensor size it was designed for, and whether it is compatible with the body's mount.

How do you choose the distance for a portrait?

In Lesson 12.4 we saw that distance, not the lens, decides a face's proportions. The crop factor doesn't change this calculation, but it does change where you stand for the same frame. To build a shoulder portrait on APS-C at 85 millimeters that you build on full frame at 85 millimeters from a few meters, you need to go farther back; to stay at the same distance, you need to use a lens of about 55 millimeters.

What matters is to stand at a distance that leaves the face's proportions even, and to choose for your sensor the focal length that gives the frame you want from that distance. Whichever face you photograph, brown or light, the order is always the same: first distance, then lens. Because the slice of sharpness is deeper on a small sensor, the background is more distinct; building a brightness difference between skin and background to separate the face from the background matters even more here.

Visual evidence

You go back to the coppersmiths' bazaar. The coppersmith is brown-skinned and broad-shouldered, their apron stained with soot; each time the hammer comes down it leaves a small glint on the surface of the pot. In the 50-millimeter frame on the full-frame camera, the coppersmith's whole bench, dozens of pots hanging on the wall and the shop's open door behind can be seen. In the frame taken with the same lens on the APS-C camera from the same place, though, the coppersmith's face, shoulders and the hands holding the hammer fill the frame; the pots at the edges have left the frame.

The two frames were taken with the same exposure: f/2.8, the same shutter speed, the same ISO. But in the APS-C frame, the pots behind the coppersmith are more distinct, the slice of sharpness deeper. To build the same frame with the full-frame camera, you come a few steps closer to the coppersmith; this time the pots behind soften more, but because you came closer, the coppersmith's face looks a little bigger relative to the background. The same lens, the same coppersmith; what changed was how big a piece of the lens the sensor took.

Common mistakes

Summary

The crop factor is the ratio of the full-frame sensor's diagonal to a sensor's diagonal: between 1.5 and 1.6 on APS-C, about 2 on Micro Four Thirds. A small sensor changes not the lens's focal length but the piece it takes from the image circle; a 50-millimeter lens on APS-C gives the angle of view of about 75 millimeters on full frame. The aperture is the same on every sensor in terms of exposure, but for the same frame the slice of sharpness deepens on a small sensor; for a portrait, first the distance that keeps a face's proportions on every skin is chosen, then the focal length that gives the wanted frame from that distance is found for the sensor.

Mini assignment

In this assignment you will find and use your own camera's crop factor.

1. Find out your camera's sensor size and write down its crop factor.
2. Multiply the focal lengths of your lenses or phone cameras by the crop factor and write their full-frame equivalents in a list.
3. Calculate which focal length your sensor needs to photograph a face from a few meters with a shoulder-level frame, and try it.
4. Photograph the same person with the same frame, first with a wide aperture from far away, then with a shorter focal length up close, and compare the sharpness of the background.

Check yourself

• Were you able to put your lenses' full-frame equivalents into a list?
• With the focal length you calculated, were you able to build the frame you wanted from a distance that keeps the face's proportions?
• When the background was more distinct, what did you do to separate the light or dark face from the background?

Glossary

Mini quiz

1. When a 50-millimeter lens is put on an APS-C body, what does its focal length become?

• A) It becomes 75 millimeters
• B) It becomes 33 millimeters
• C) It stays 50 millimeters; only the angle of view resembles about 75 millimeters on full frame
• D) It becomes 100 millimeters

2. On a Micro Four Thirds camera, a 25-millimeter lens gives the angle of view of roughly which focal length on full frame?

• A) 12 millimeters
• B) 50 millimeters
• C) 25 millimeters
• D) 100 millimeters

3. How does an f/2 lens behave in terms of exposure in the same scene on a full-frame and an APS-C body?

• A) It gives the same exposure with the same shutter speed and ISO
• B) It shoots two stops darker on APS-C
• C) It shoots one stop brighter on APS-C
• D) It doesn't work on full frame

4. On an APS-C camera, what do you do to build a shoulder portrait from a distance of a few meters that keeps the face's proportions?

• A) Come very close to the face and use a wide angle
• B) Keep the distance and choose a shorter focal length, taking the crop factor into account
• C) Raise the ISO
• D) Change the white balance

Answers

1. C — Focal length is a physical property of the lens; a small sensor only takes the middle of the image.
2. B — On Micro Four Thirds the crop factor is about 2; 25 × 2 = 50 millimeters.
3. A — The f-number describes the intensity of light falling on every point of the sensor; it is independent of sensor size.
4. B — Distance decides proportions; to build the frame from that distance, a focal length suited to the sensor is chosen.

Summary card

• Crop factor = full-frame diagonal ÷ sensor diagonal: APS-C ~1.5–1.6, MFT ~2.
• Focal length doesn't change; only the angle of view narrows.
• Equivalent field of view = focal length × crop factor.
• f/2 gives the same exposure on every sensor; for the same frame, sharpness deepens on a small sensor.
• Portrait: first the distance that keeps proportions on every skin, then the focal length suited to the sensor.

Bridge to the next lesson

In the coppersmith's APS-C frame, the pots behind were more distinct than on full frame; the slice of sharpness was deep. When you want to melt the background, or shoot in a dim shop without going up to high ISO, the most powerful tool left in your hand on a small-sensor camera is the lens's maximum aperture. Why a relatively affordable lens with a wide aperture such as f/1.8 is recommended so often, and the limits of this recommendation, are the subject of the next lesson: maximum aperture.