Approximate Distance Calculation for Bird Photography

Often times people will ask me how far away I was from a bird in a given photograph.  In many cases it is not possible to accurately measure the distance due to physical obstacles or having the question asked after the fact when one is no longer at the photography site.

The request to know the distance is common and I often find myself asking the same question when examining photos.  Approximating the distance to a bird is a reasonably straightforward geometry calculation but does require some knowledge of the photographic equipment being used and size of the bird being photographed.  Following are the information needed for the calculation:

S - bird size in whatever measurement units one is comfortable (i.e. metric or English).  For most birds this information can easily be found in reference books or on the internet.  Bird books commonly list the length of a bird and the outstretched wingspan.  Either of these can be used based upon the photograph being analyzed.

A - the viewing angle.  Viewing angle information is typically supplied by camera manufacturers and has a different value for vertical and horizontal.  Most of my photos have the birds measurable in the vertical dimension so I will use this value.

C - Crop factor of the camera.  This number represents a relationship between the size of the sensor and a 35mm film sensor.  This information is available from most camera manufacturers.

PC - Pixel Count - the number of pixels in the camera sensor.  This will have a value for both the vertical and horizontal dimensions.  Since I am using the vertical dimension for this analysis I will use the vertical pixel count.

SPS - the measurement of the subject size in pixels.

With the above it should be possible to estimate distances given a subjects size (in pixels) on any given photograph.  Let's look at a couple real life examples.  First up is the photograph below of a Red-shouldered Hawk taken in my backyard (so I could measure the distance to see how accurate the calculations were).

The picture was taken using a Canon 500mm lens with a Canon 7D camera body.  Since the bird sizes are approximate I will use reasonably close estimates for purposes of these calculations.  One can be as accurate as they like, but there will always by some amount of uncertainty about the subject's dimensions so being overly precise is not really worth the effort.

The National Geographic Complete Birds of North America guide lists the length of a Red-shouldered Hawk as varying between 15 and 19 inches.  Since I don't know the exact size I will take a value of 17 inches and know that the calculation can be off as much as +/- 10%.  So:

S = 17 inches.

A =  2 degrees 45 seconds.  This converts to 2.75 degrees.  Information available from Canon web site or I used Wikipedia.

C = 1.62.  This is the crop factor for the Canon 7D camera.  Information available from many photography web sites.

PC = 3456.  Information from the Canon web site.

SPS = 1200.  Measured from the photograph.

The distance, D, to the subject can be calculated using the following formula:

D = (C * S * PC)/(tan(A) * SPS), where tan is the geometric tangent function.

Substituting in values from above we see:

D = (1.62 * 17 * 3456)/(tan(2.75) * 1200) - performing appropriate calculation yields:

D = 1,651 inches.  This converts to 137.6 feet.  Actual measurement for this photo was 135 feet so it was pretty accurate.

Hopefully this approach helps you answer the question "How far away was that bird?" the next time someone asks.