Crop factors explained

It’s still relevant for translating the listed focal lengths of lenses into 35mm equivalents, with respect to the camera’s sensor.

‘Crop’ is a useful term because for a given lens and subject distance, subjects will be imaged at the same size on the sensor plane. The smaller the sensor, however, the larger the proportion of the frame the subject occupies, as shown in this illustration.

The actual resolution of the image sensor is irrelevant; what matters is the relationship between the sensor size and lens focal length. The smaller the sensor format, the shorter the focal length must be to capture the same angle of view as the same focal length on a 35mm camera.

The illustration above shows how smaller sensor sizes ‘crop’ the image area and provide a narrower angle of view than the same lens on a 35mm camera, which is represented by the entire frame.

Crop Factors and Focal Length

Crop factors make telephoto lenses appear more powerful on cameras with smaller sensors because the angle of view is reduced. You can calculate the equivalent 35mm focal length by multiplying the listed focal length of the lens by the sensor’s crop factor.

However, when you fit a 100mm lens onto a camera with a smaller-than-35mm sized sensor, it’s still a 100mm lens. What has changed is the format of the sensor, which covers a smaller field of view and makes the lens behave like a longer lens.

For an APS-C sensor, the crop factor is approximately 1.5x, which means a 100mm lens will behave like a 150mm lens. With a M4/3 sensor, the crop factor is 2x, yielding a focal length equivalent to 200mm in 35mm format. The 1-inch sensor’s crop factor of 2.8x and the digicam’s crop factor of approximately 6x cover focal lengths equivalent to 280mm and 600mm, respectively.

Designing telephoto lenses with focal lengths of 200mm and 300mm is relatively straightforward for APS-C and M4/3 cameras as long as fast maximum apertures aren’t required. Sports and wildlife photographers can achieve tight subject framing from a longer distance with telephoto lenses on sub-35mm sized sensors. (Lenses for smaller sensors can also be smaller, lighter and cheaper to produce.)

Crop factors help to explain why it is more difficult to produce really wide-angle lenses for cameras with small sensors, particularly APS-C DSLRs which require space between the back of the lens and the sensor for an SLR mirror.

This table lists a range of popular wide angle focal lengths for 35mm cameras and shows the equivalent focal lengths for different sensor sizes.  

Perspective is not affected by crop factors. Many people think the perspective distortion associated with wide-angle lenses is due to the lens itself; but it’s actually created by the distance from the subject to the lens. Consequently, with the same camera-to-subject distances, a shot taken with a 23.3mm lens on an APS-C camera should cover the same field of view and have the same perspective as one taken with a 35mm lens on a full frame camera.

The areas from the different image sensor sizes, re-sized to the same dimensions, show the telephoto effect of the smaller image sensors ““ for a specific focal length and camera-to-subject distance.

Crop Factors and Depth of Field

Depth of field refers to the range of distances that appear acceptably sharp in an image. It is determined by the size of the image sensor with respect to the distance to the subject and the lens aperture setting. If you fill the frame with a particular subject, depth of field will decrease for a given aperture as progressively larger sensors are used to record the image because larger sensors require you to move closer the subject to maintain the same size in the frame.

Suppose you’re taking a portrait with a 100mm lens on a 35mm camera and set the aperture at f/4 to ensure most of the face is acceptably sharp. To shoot the same portrait with an APS-C camera, you would need a 66mm lens with the aperture set at f/2.6. On an M4/3 camera, you’re looking at a 50mm lens at f/2 and on a digicam with a 5x crop factor the focal length is reduced to 21mm with an aperture of f/0.8 (which is not possible with consumer lenses). This is why compact cameras struggle to produce significant background blur in portraits.

A shallower depth of field may be desirable for portraits because it improves background blur. However, a wider depth of field is preferable for landscape photography.

Suppose you’re shooting a landscape with a 24mm lens at f/11 on a 35mm camera. To shoot the same scene with an APS-C camera, you would need a 15mm lens with the aperture set at f/6.9. On an M4/3 camera, you’re looking at a 12mm lens at f/5.5 and on a digicam with a 5x crop factor the focal length is reduced to 5mm with an aperture of f/2.3. This is why compact point-and-shoot cameras and camera-phones have almost unlimited depth of field.

These simulations demonstrate the large depth of field available with small-sensor digicams (top), compared with cameras that have larger sensors. All three shots cover roughly equivalent focal lengths and have the same aperture setting: f/2.8.

Crop Factors and Image Quality

Nearly all lenses are sharpest in the centre of the frame, although many suffer from noticeable edge and corner softening. When a lens designed for a camera with a 36 x 24mm sensor is used on a camera with a smaller sensor, the soft edges are cropped away, so affected lenses should produce better results on cameras with smaller sensors.

Interestingly, lenses that are used on cameras with smaller sensors must perform better than 35mm lenses. Since the image is magnified when it’s projected onto the smaller sensor, higher resolution will be required to match the quality of equivalent 35mm lenses.

Larger sensors can also tolerate smaller apertures before diffraction begins to reduce sharpness. However, the onset of diffraction is gradual and it may not be noticeable until a stop or so beyond the theoretical limit so it may go undetected. The theoretical limits for a range of sensor resolutions are shown in the table below.

In practice, this means you should obtain optimal sharpness over a wider range of apertures with a larger sensor camera. The theoretical diffraction limit for depth of field becomes lower as resolution increases, a factor to take into account when choosing your next camera.

More pixels may not necessarily provide better resolution at smaller lens apertures. In fact, more pixels could affect image quality by increasing noise and reducing dynamic range.

Crop Factors and Camera Shake

Crop factors have no impact on the actual positional displacement caused by camera shake. However, because the viewing angle is reduced with higher crop factors, camera shake is usually more noticeable.

With a 200mm tele lens on a M4/3 camera, the angle of view is approximately six degrees. Shake the lens by only three degrees and the subject will be displaced in the frame by half the field of view.

To minimise the potential for camera shake with an unstabilised lens, use the reciprocal of the focal length as the minimum shutter speed. For example, the minimum shutter speed for a 200mm lens is 1/200 second.

For smaller sensors, you can calculate the applicable minimum shutter speed by applying the crop factor. In the case of the 200mm tele lens on a M4/3 camera, the crop factor of 2x means the minimum shutter speed should be 1/400 second.

Lenses that include optical stabilisation can usually provide at least two stops of stabilisation, enabling photographers to use shutter speeds of 1/100 second or slower with a 200mm tele lens on a M4/3 camera and expect a high percentage of acceptably sharp shots.

This shot of a leopard was taken just before sunset (which accounts for the warm colour cast). The very low light level would have required a shutter speed of at least 1/600 second with the 300mm telephoto lens but effective stabilisation provided more than two-stops of compensation and produced a sharp image at 1/160 second.