Shadow from a sun angle
Works in any unit: feet in, feet out. The ratio column below is unit free.
Shadow at a real place and time
Worst case: solar noon in December
This is the number that matters when buying a plot or planting a hedge. If the December noon shadow of a neighbouring building reaches your windows, no amount of summer sunshine will fix it. Model the exact geometry on the sun position map.
Shadow ratio table
Multiply the object height by the ratio to get the shadow length.
| Sun altitude | Ratio | Shadow of a 2 m person | Shadow of a 10 m tree |
|---|
Where shadow length decides things
Buying a plot or a flat
Sellers show photographs taken in June. Ask instead what happens at noon on 21 December: a five storey block 20 m to the south at 52° latitude casts a shadow around 60 m long, which swallows an entire garden. The map tool reports the shaded hours for that date directly.
Solar arrays and row spacing
Ground-mounted rows must not shade each other at winter noon. The clear distance is the panel's vertical height divided by the tangent of the December noon altitude, times a correction for the azimuth spread you want to protect. That is why solar farms at high latitudes look so spread out.
Gardens and greenhouses
Most vegetables want six hours of direct sun. Check the shadow of the house and the fence in March and September rather than in June, because those months bracket the growing season and the sun is already 20–30° lower than at midsummer.
Photography and forensics
A shadow in a photograph encodes the time it was taken. Measure the ratio of shadow to object, take the arctangent of its inverse to get the altitude, and match it against the sun path for that date and location on the sun path page.
Questions
Frequently asked questions
How do you calculate shadow length?
Shadow length equals the object height divided by the tangent of the sun's altitude angle. A 10 metre tree with the sun 30 degrees above the horizon casts a shadow of 10 / tan(30 degrees) = 17.3 metres, pointing in the direction opposite the sun.
In which direction does a shadow fall?
Directly away from the sun: the shadow azimuth is the sun azimuth plus 180 degrees. With the sun in the south-east at 135 degrees, shadows point north-west at 315 degrees. At solar noon in the northern hemisphere shadows point true north, which is how a sundial or a shadow stick finds north.
When are shadows longest?
At sunrise and sunset, when the altitude approaches zero and the shadow grows without limit. For a usable worst case, planners use solar noon on 21 December: at 52 degrees north the sun is only about 14 degrees up, so every object casts a shadow four times its height even at midday.
How long is a shadow at 45 degrees?
Exactly as long as the object is tall, because tan(45 degrees) = 1. That makes 45 degrees a handy mental benchmark: above it shadows are shorter than the object, below it they are longer.
How far from a building should I plant a tree?
Take the mature height of the tree, divide by the tangent of the December noon altitude at your latitude, and that is how far north of the building the shadow reaches at midday. The calculator does this for your coordinates in the winter worst case box.