1. Math in Photography © UNT in partnership with TEA
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© UNT in partnership with TEA
AAVTC: Commercial Photography – Shutter Speed
AAVTC: Commercial Photography – Shutter Speed

2. Math in Photography
Math abounds in photography in ways that make it seem easy.
Without thinking, a photographer will think in terms of complex mathematical equations as they adjust their aperture, ISO, and shutter speed.
An important, but lesser known mathematical relationship in photography is with focal lengths.
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3. What Focal Length Isn’t
The last time we spoke about focal length in-depth was when we discussed lenses.
Many people just associate focal length as being how “zoomed in” a particular lens is.
While it is true that the higher the “millimeters” of a lens, the more “telephoto” the lens is considered, the actual definition of focal length measures something else.
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4. What is focal length?
Focal length is the distance in millimeters from the optical center of a lens to the sensor at the back of the camera.
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5. 35mm Equivalent
You may have come across the term "35mm equivalent" when looking at focal length before.
This term is based upon old film cameras that used 35mm film.
The term exists to describe the field of view with a lens through cameras that have different sensor sizes.
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6. Example
It used to be that no matter what camera you put it on, a 28mm lens would give you the same field of view.
However, with the advent of digital cameras, there is no universal relationship between the focal length of a lens and the angle of view that is received.
Since the size of a camera’s sensor determines the angle of view, a 28mm lens on a film camera would not produce the same image as a 28mm lens on a small digital camera.
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7. Cameras with Different Sensor Sizes
The camera on the right has full frame sensor, while the camera on the left has a cropped sensor.
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8. Different Sensor Sizes
Sensors come in all different shapes and sizes.
The size and shape of a camera’s sensor determines the “aspect ratio” of the photos it produces.
For example, most medium or large format cameras have a square sensor and produce images with a square aspect ratio because they have a square shaped sensor.
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9. Cropped vs. Full Frame
Most modern day camera sensors fall into two categories:
Full Frame Cameras
Cropped Sensor Cameras
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10. Full Frame Sensor
Full Frame Sensor – Full frame sensors are the same size and shape as 35mm film. Therefore, a lens with a focal length of 50mm would look the same on both an old film camera and a modern day DSLR with a full frame sensor. Its focal length is 50mm no matter what.
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11. Cropped Sensor
Cropped Sensor – A cropped sensor is a sensor that produces images that are a different shape than a 35mm film. It is almost as though the sensor has been “cropped,” or had a portion of it cut off. For this reason, the field of view is smaller than a full frame camera.
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12. Field of View
In the image on the right, you can see that the red sensor sees a larger portion of the image than the blue sensor, even though they both have the same focal length.
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13. Field of View
The red rectangle is a full frame camera, which has a larger sensor and therefore sees “more” of the image than the blue, cropped sensor camera. It has a wider “field of view.”
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14. Buying a Lens
Most lens sizes are named according to what they are on a full frame camera.
For example, a 50mm lens would have a focal length of 50mm on a full frame camera, but not on a cropped sensor camera.
Keep in mind what type of sensor you have when purchasing a lens so you know what the true focal length will be.
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15. Crop Factor
“Crop Factor” measures how far a cropped sensor is from a full frame sensor.
Most cropped sensors have a crop factor of either 1.6 or 1.5.
Mirrorless cameras have a crop factor of 2.
This means that a 40mm lens would actually have a focal length of 80mm on a mirrorless camera.
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16. Other Ways Photography Deals with Math
Equivalent focal lengths are just one of the many ways that photography deals with math.
Many of the other ways are like second nature to seasoned photographers, such as yourselves.
A photographer will adjust aperture, ISO, and shutter speed while keeping in mind the inverse relationship that exists between them and light.
The seasoned photographer will also keep in mind their depth of field and how their aperture, focal length, and distance from subject affect the photograph.
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17. Review
Focal length is often different, depending on the size of your sensor.
Sensors that are the size and shape of 35mm film are called “full frame” sensors.
Sensors that are smaller than 35mm film are called “cropped” sensors.
Different sensors have different “crop factors.”
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