Rudy Winston
Rudy Winston

Rudy Winston has over 16 years experience with Canon USA's Pro Products team, and has been responsible during that time for training Canon's staff on new products, creating presentations for customers and dealers, numerous writing projects, and providing technical assistance to professional and amateur photographers.

Which lens do I need? Calculating lens and image sizes: Part II

August 20, 2013

We started off last week with a basic layout of formulas, terms and sizes. This week in Part II, we discuss how to apply what you’ve learned to shooting situations you may have or will experience.

Answering the question: “Which lens do I need?”
Lens focal length needed = Image Size x Distance, divided by Object Size

For example: you’re going to shoot a pro baseball game from the first base photographer’s area. You know that area is roughly 120 feet from home plate at your team’s park or stadium. And you know you want to fill the horizontal frame with batters at home plate — perhaps a bit more than 6 ft tall, on average.

  • Image size (in this example, we’ll assume a full-frame camera and horizontal shooting) would be about 20mm.
  • Distance is 120 feet. Converted to millimeters, that’s about 36,600mm (it’s obviously okay to approximate figures here!)
  • Object size — actual size of our object or subject — is 6 ft tall. Converted to mm, that’s about 1,830mm (again, it’s okay to approximate for subjects that are “normal” distances or greater from the camera)

With the rough numbers converted to millimeters, pull out the calculator:

Lens focal length needed = 20mm x 36,600mm, divided by 1,830mm

Lens focal length needed = 732,000mm, divided by 1830mm

Lens focal length needed = 400mm

You’d need a 400mm lens to get this image size of that subject, from about that distance!

With a particular lens, how far or close will I need to be?
Distance = Lens focal length (mm) x Object Size, divided by Image Size

Another hypothetical example: you know you have a 200mm lens and you use an APS-C camera, like an EOS 60D or EOS 7D. Because friends and acquaintances know you’re an accomplished shooter, they’ve nominated you to shoot their child’s elementary school play. You know you want to get some tight, full-length, vertical images of first and second graders — who are perhaps 50 inches (a bit over 4 feet/1.2 meters) tall. How far away from the stage should you ask them to reserve a seat for you?

  • Lens focal length is 200mm. That’s based on the lens the shooter already owns, in this hypothetical example.
  • Object size — 50 inches (1.2m) is the actual subject height and converted to millimeters is 1,270mm… 1,300mm is close enough for our purposes!
  • Image size on the actual CMOS sensor is going to be about 18mm — full-length, vertical shots with an APS-C sensor camera (total available height on the sensor, held vertically, is about 22mm; 18mm would allow comfortable composition with room above and below the final subject).

To calculate:

Distance = 200mm x 1300mm, divided by 18mm

Distance = 260,000mm, divided by 18mm

Distance = 14,444mm

(Convert that back to feet by dividing it by the number of millimeters in a foot — 304.8)

14,444mm divided by 304.8mm = 47.4 feet.

You’d need to be about 50 feet away to get the tight, vertical shots of those grade school kids you’re hoping for with your 200mm lens.

Looking back at an existing picture: How big was that actual subject?
Object size = Image Size x distance, divided by Lens focal length

One more hypothetical example: You and your family went to a National Park a year or two ago and got a guided tour by a park ranger. Along the way, you photographed (from a distance) a mother bear and her cubs. Recalling the moment, you wonder just how big that bear really was. And you remember asking the park ranger at the time how far you were from the bears, to which the reply was about 75 yards. You shot images with your APS-C EOS Rebel camera and your EF 70-300mm zoom lens at 300mm.

While looking at a full-resolution image on your computer screen, a quick measurement on-screen shows a side view of the mama bear who takes up about 60% of the image’s total width — because you know from reading a blog post on Canon’s Digital Learning Center, your sensor’s image area is about 22mm total in width, meaning the bear takes up about 60% of that — an image size of 13.2mm.

  • Image Size is 13.2mm. You quickly established that by doing an on-screen measurement of your full, original image file’s width and how much of the frame side-to-side was occupied by the subject.
  • Distance is 68,580mm. 75 yards multiplied by 914.4 (number of mm in a yard).
  • Lens focal length is 300mm. Even if you don’t remember exactly, you usually can get this information from the EXIF text data that can be displayed in browser software from Canon and other makers.

To calculate:

Object size = 13.2mm x 68,580mm; divided by 300mm

Object size = 905,256; divided by 300mm

Object size = 3017mm (3000mm would be close enough for our purposes!)

(Convert 3000mm to feet by dividing by 304.8 — the number of mm in a foot)

The actual size of the bear, front to back, is about 9.8 feet — good thing you were a fair distance away!

Summary

Mathematicians among our readers or my high school math teachers, for that matter, will doubtless tell us that even more precise answers can be derived by more complex calculations which include angle of view and so on. But the three equations here provide quick and relatively easy to obtain answers to three distinct questions. The first one is probably the one most users would want to get an answer to: “Which lens do I need?”

The answers here are approximate and, once again, assume normal and longer shooting distances from a subject. For exact magnification calculations for precise close-up or macro shots of small objects, different and more detailed calculations are required — and available from both written and online technical sources. Our discussion here intends to provide quick and general answers to common questions and situations.

By doing some fast figuring, you can come up with answers to help narrow down lens choices the next time you’re either in the market for a new lens or presented with a particular shooting scenario that needs a clear answer to that same basic question. And using the same types of info, you can get general answers to a couple of other questions you might occasionally be presented with.

And one more – just in case you ever need to figure out how much of the frame you’ll cover, with a specific lens and from a specific shooting distance:

Image Size (on the sensor or on film) = Lens focal length x Object size; divided by Distance.

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