# What is the formula for percent of frame filled at a specific distance and focal length?

I am thinking about buying a new lens specifically to take photos of distant targets (birds, bears, etc). I currently own the Canon 70-300 IS USM, which is a nice lens, but I find that if I want to take a photo of anything further away than about 10 meters, the target does not fill a large amount of the frame (meaning I have to significantly crop in post production).

I am currently looking at the Canon prime 400mm, however I would like to determine at what distance an object will fill a reasonable proportion of the frame.

Is there a formula or rule of thumb I can apply that will help me in this situation? I realise the size of the target I am shooting will play a role here, so if we need to make an assumption about the size of the target please let me know.

• SOH-CAH-TOA - en.wikipedia.org/wiki/Trigonometry#Mnemonics Commented Aug 26, 2011 at 22:19
• Unless you're using a circular fisheye lens or one not designed for your camera, 100% of the frame will be filled at any distance and focal length. Commented Mar 30, 2016 at 15:31

The formula for the percentage of image filled is

focal_length x subject_size x 100
_________________________________

distance x sensor size


All units are millimeters. Use the width of the subject/sensor to work out the horizontal fill % and the height of the object/sensor to work out the vertical fill %

• Actually you could have distance and subject_size in larger units, as long as you use the same unit for both.
– Imre
Commented Aug 24, 2011 at 17:01
• Good point. You can also express the sensor size and focal length in any units you please (as long as they match): cubits, furlongs, AU... Commented Aug 24, 2011 at 17:04
• Sure, but focal length is quite universally in millimeters, so it makes sense to measure sensor size in millimeters as well.
– Imre
Commented Aug 24, 2011 at 17:14
• @Imre well I typically refer to my sensor as 1.3369113537530945319991403659995e-13 AU wide. ;) Commented Aug 24, 2011 at 17:18
• Astronomical units are probably the best unit of measurement to use, IMHO. Sorta. Ok, not really. Commented Aug 25, 2011 at 2:07

Here's the nice thing — the relationship between focal length and sensor size are directly related in a simple way: If you double the focal length, that's exactly like cropping in half (in each dimension, so a quarter of the area).

That means if you put your existing lens at 300mm, and then crop to 75%×75%, you'll see what a 400mm lens will get you, since 300 is 75% of 400.

(Or 200mm and cut in half, but 300mm is easy with your 70-300mm lens.)

• +1 -- the simple ratio is much more practical in the field (the full-on formula is great under more controlled conditions). Simply knowing that you need 600mm worth of lens (either a 600mm prime or a fast 300mm with a doubler) to make something twice as big as it appears at 300mm can make getting closer a much easier decision to make.
– user2719
Commented Aug 24, 2011 at 19:32
• Then it's just a matter of saving \$10,000 for a 600mm lens :) Commented Aug 25, 2011 at 2:17

@Matt Grum has the full-blown formula. Here's the rule of thumb I use for finding frame coverage in the field.

1. Choose your preferred fill direction: horizontal or vertical.
2. Know your sensor size in this direction.
• Wikipedia has a good list of sensor sizes.
• This should be relatively easy to memorize, since there's only two numbers for a given camera/sensor.
• Of course, camera orientation matters. If you're holding your camera sideways (ie: "portrait mode"), and you want to fill the frame vertically, you'll want the sensor width, not height.
3. Divide your lens' focal length by this sensor size dimension. This gets you a ratio/multiplication factor.
4. Multiply the size of the subject by the ratio in step #3 to get the distance to the object for 100% coverage.

You can easily trade off distance, focal length, or fill percentage depending on your shooting circumstances.

So, for example, let's say I want to take a full-body shot of a person that's 2m tall. My APS-C Nikon D90 has a sensor that's about 24mm wide. If I shoot with my 50mm lens, I know that it has roughly a 2x distance factor to it... so I want to be at least twice as far away from my subject as he is tall: 4m. If I only have 2m to work with, then I'll need a 24mm lens, or shoot only his top half.

Assuming you have an APS-C Canon sensor, then the full 300mm zoom on your lens would give you a distance factor of about 20 (in landscape/wide orientation). If you only fill 50% of your frame height, you'll need to be 4m away from a 10cm-high bird; that doesn't seem like a lot to me. That's why serious birders use huge telephoto lenses and teleconverters; they need every bit of magnification to capture their tiny subjects from far away.