Calculate Shadow Length and Direction

For a simple calculator without coordinates and time, see shadow casting.

Shadow length

Visualisation

h = height of the object which casts a shadow
α = altitude of the Sun above a flat horizon
l = length of the shadow
h and l have the same unit, like meters or feet.
l = h * sin(90°-α) / sin(α)

The result is an estimation, which especially at low Sun altitude can be inaccurate!

Calculator for the length and direction of a shadow at a given date, time and place. For an exact calculation, the true local time and the exact coordinates should be used. The coordinates of a certain location can be found out by right clicking in Google Maps on the location and choosing "What's here". Please enter decimal degrees, you can convert other specifications with the Geo Coordinates Converter. For the time of day, daylight savings should be ignored.

The output are the length of the shadow, the altitude of the Sun in degrees and the direction of the shadow as compass points and as degrees. The direction of the Sun, the azimuth, is exactly opposite (± 180°). If the shadow is directed at 260 degrees, for example, then the sun is at 80 degrees, i.e. east-southeast, and it is then morning.

Calculating the length and direction of a shadow based on location and time is actually quite complicated. A source code that carries out this calculation and on which this calculator is based can be found on a corresponding discussion page on the developer platform Stackoverflow. This source code, which has been adapted for the calculation here, is not completely error-free, the results are subject to a certain degree of uncertainty and should really only be viewed as an estimate.