How to work out the time of day from a shadow in a photo

Measure something in the picture whose height you know and the shadow it casts, in the same units, and divide: the shadow's length over the object's height is the tangent of the sun's angle below vertical, so a shadow as long as the object means the sun was 45° up, and one twice as long means 27°. Then find which way the shadow points, using anything in the frame that gives you north. The sun's height and bearing are computable for any place, date and minute, so the pair you measured picks out the minutes of that day when the sun stood there — usually two windows, one before noon and one after, and the direction says which. A claimed time either falls inside a window or it does not.

The two measurements

The ratio. You do not need the object's real height, only the proportion. A person, a door, a lamp post, a car: anything with a known or guessable height standing on flat ground, with its shadow on the same flat ground, running away from the camera as little as possible. Measure both in pixels on the photograph, or with a ruler on a print, and take shadow over height. A shadow measured off a photograph is good to perhaps five per cent on a good day, and that is the number that decides how wide the answer is, so measure the largest clean shadow in the frame.

The direction. Which way, in compass terms, the shadow points. A street on a map, the face of a building, a road sign, the sun's glint on a known feature: anything that fixes north in the frame. The direction is what turns one answer into two, because a shadow of a given length falls twice a day, once as the sun climbs and once as it falls, and it points the opposite way each time.

A worked example

Central London, 21 June 2026, a 1.80 m post with a 1.75 m shadow. The ratio is 0.97, which puts the sun 45.8° above the horizon. On that date at that place the sun is that high twice: around ten in the morning, in the east-south-east, and around four in the afternoon, in the west-south-west. Allow five per cent on the length and ten degrees on the direction, and SHADOW gives the two windows as 09:54 to 10:13 and 15:52 to 16:10 British Summer Time. The shadow points west-north-west, so it is the morning one.

Now the claim. The picture is said to have been taken at nine. At 09:00 the sun is 36.3° up, the shadow would be 1.36 times the post's height pointing west, and what was measured is 0.97: the picture and the claim disagree, and the shadow is consistent with ten past ten instead. Said to be 10:05, they agree. Those are the two possible outcomes, and they are not symmetrical: a disagreement is a finding, and an agreement is only the absence of one. The same shadow also falls on many other dates, so agreement supports the story rather than proving it.

A disagreement is not a forgery, either. A camera clock never set, a time zone wrong by an hour, a location a few streets from the one assumed — all of those produce a shadow that does not match the claim without anybody having lied. The finding is that one of four things is wrong: the place, the date, the measurement, or the story. Which one is a separate question.

Why the sun is a better witness than the metadata

The time in a photograph's metadata is whatever the camera's clock said, which is whatever somebody last set it to, and it is editable with any number of free tools. Most of the apps a photograph travels through strip it anyway. The sun's position on a given date at a given place is fixed by orbital mechanics and computable to a hundredth of a degree with the standard algorithm, which is far finer than a shadow can be measured, so the error that matters is always the measurement and never the arithmetic. It cannot be changed after the shutter closed, and it does not care what the file says.

What a shadow cannot tell you

• The date. The sun retraces its path either side of a solstice, so every shadow except the two extremes is consistent with two times of year. Narrowing the date takes a second shadow at a known interval, or something else in the frame: foliage, snow, what people are wearing.
• The minute. A five per cent error on the length is about a twenty-minute window in the example above, and more when the sun is low, because a long shadow changes length slowly. A single time quoted to the minute from a measurement that loose is a lie with a decimal point in it.
• Anything without the place. The same shadow means different times at different latitudes. If the place is not known to within a few tens of kilometres, the answer is not known either.
• Anything from a low sun. Below about ten degrees the shadow is too long to measure and the atmosphere lifts the apparent sun by up to half a degree. The page does not correct for refraction, because a shadow long enough for it to matter is too long to be useful.

What SHADOW does and does not do

SHADOW takes the place, the date, the clock offset, the object's height, the shadow's length and the direction it points, with the tolerance you allow on each, and returns the windows of the day that could have cast it, the sun's height and bearing in each, and a verdict on the time claimed. It also works forwards: give it a time and it says what the shadow should have looked like. The astronomy is the NOAA solar position algorithm written out in full so that every constant can be checked, and it is checked on every build against the same algorithm written again from the published terms, on sunrise, sunset, the noon height and the two windows above.

It runs in the browser and sends nothing, which is not a convenience for this job. The place a photograph under investigation was taken is frequently the single most sensitive fact about it, and the usual way of doing this is to type that place into somebody else's map. It does not find north for you, measure the shadow for you, or tell you which of the four things is wrong when they disagree.