Working with Shadows in a Photograph

The Basics

To calculate the time of day (ToD) and day of the year (DoY) that a photo was taken, you need to know three things:

  1. The latitude and longitude of the location of the object whose shadow you are using for your calculations,
  2. The angle the sun is above the horizon (its elevation),
  3. The angle the sun is east or west of its position at noon (its azimuth).

Elevation Angle of the Sun

Sometimes it is easy to figure out the position of the sun from the shadows in a photograph, and sometimes it is more difficult. It depends on whether the camera was directly facing the object that was casting the shadow, and whether the object was on the same level as the camera.  In either case, a correction must be done for perspective. We won’t address this here, to keep things simple.  If you have a shadow you would like some help in correcting for perspective, please write to me at Assuming that either you have a shadow that does not need correction for perspective, or that has already been corrected, you will need an ephemeris to find the ToD and DoY based on that shadow.  According to Wikipedia (, an ephemeris is a table of values that gives the positions of astronomical objects in the sky at a given time or times. An easy-to-use solar ephemeris that is handy for finding the ToD and DoY from shadows is found at


Home page of the Great Circle Studio’s solar ephemeris set up to calculate the ToD and the DoY for the Sheboygan Dead Horse photo.

Usually, you must supply an ephemeris with the ToD and the DoY for which you would like to calculate the position of the sun.  However, to analyze a photo,  you want to do the reverse – you want to find the ToD and DoY based on the sun’s position.Since the Great Circle Studio Solar Calculator cannot be run backwards, to use it in reverse, you must enter a guess for ranges for the ToD and DoY and allow the calculator to produce the position of the sun over this range. If the solar positions that are output do not match the ones you have calculated from your photograph, you can adjust the input to the calculator and run it again. You can continue adjusting your input ToD and DoY until you obtain a solar position that comes close to the one you want. This will be associated with the ToD and DoY when the photo was taken.

An Easy Example

The Sheboygan Dead Horse Picture

An easy example of how to do this is provided by the Sheboygan Dead Horse photo. The man in the photo is sitting at the intersection of Griffith and Indiana Sts. The camera is pointing to the north along Griffith St. in the direction of the Sheboygan River.

Shadows lie directly to the east on Griffith Ave.

In the image, the shadows in the picture fall directly to the east across Griffith St, implying that the sun is directly in the west at an azimuth of 270 degrees. Having the sun in the west and the camera facing north and aimed directly at the man on the horse means we don’t have to correct the length of the shadows for perspective.

Calculating the Angle of the Sun

Finding the elevation of the sun is also easy using the triangle outlined in red in this image. As stated above, the angle of elevation is THETAe = arctan (H/L). We only need relative measurements of the legs of the triangle, not absolute.  Using our high resolution version (too large to post), and shortening the base of the triangle to account for the gap caused by the tear in the picture, we obtained THETAe = 22.85 deg.Going back to the Great Circle Studio Calculator, we input the latitude and longitude of Sheboygan as Lat = 36 deg 37′ 05″ N, Long = 121 deg 55′ 29″ W.  We then input several guesses at the date, and had the calculations done in relatively coarse steps (indicated as “Data Interval” on the calculator), leaving the rest of the switches unchanged. We repeated inputting new dates and times based on our previous results until we pinned down August 10 as a date when the sun came close to our position of THETAa = 270 deg, and THETAe = 22.85 deg.  (It is also close to this position on May 5.)  We iterated on the ToD until we produced the chart below. Since the sun traces the same path every year to within a small error, we don’t have to worry about the year.

There is a lot of information in this table that you don’t need – so I’ve boxed in the important items in red. There is no entry that matches our parameters exactly – the closest we can come is at 16:52:03 (4:52:03 pm) when the son is at 22 deg 52′ 58″; elevation (apparent altitude), and 269 deg 29′ 43″; apparent azimuth.  Note that local civil time is different from local solar time.  But this was not important in 1871 when time had not been standardized into time zones.

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