Shadow Length Table
| Month (15th) | 30°N | 40°N | 50°N | Read |
|---|---|---|---|---|
| January | 1.25 | 1.82 | 2.95 | a 10-ft tree throws a 30-ft shadow at 50°N |
| February | 0.93 | 1.32 | 1.96 | crossing 1:1 - shadow shorter than height |
| March | 0.64 | 0.91 | 1.30 | equinox: 1.00 at 45°N exactly |
| April | 0.37 | 0.59 | 0.85 | the summer squeeze begins |
| May | 0.20 | 0.39 | 0.61 | noon shadows nearly vanish |
| June | 0.12 | 0.30 | 0.50 | solstice: half-height shadows at 50°N |
| July | 0.15 | 0.33 | 0.54 | the floor holds |
| August | 0.28 | 0.48 | 0.72 | creeping back |
| September | 0.50 | 0.74 | 1.06 | second equinox: 1:1 at 45°N |
| October | 0.79 | 1.12 | 1.61 | past 1:1 - the light year turns |
| November | 1.12 | 1.62 | 2.51 | garden shade maps redraw |
| December | 1.34 | 1.98 | 3.32 | solstice: triple shadows at 50°N |
The same tree that shaded nothing in June throws three times its height in shadow by December - and that swing, not the weather, is what quietly redraws every garden, window and solar panel between the solstices. The table gives the noon shadow as a simple ratio of object height, month by month, at three latitudes.
Bottom line: the ratio is one division - shadow equals height over the tangent of the noon sun angle - and the year's shape falls out of it. Shadows run shortest at the June solstice (half of height at 50°N), stretch longest at the December solstice (three times height at 50°N), and hit exactly 1:1 at 45°N on the equinoxes, the calendar's own calibration mark.
The honest part: these are noon shadows at their daily shortest, on flat ground, in true-sun terms. Morning and evening shadows run long past any ratio in the table, buildings slope the ground truth, and daylight saving shifts when 'noon' happens on the clock - but the ratio itself is pure geometry, the same one that put a stick and a shadow among the first measuring tools humanity owned.
How to use
- Pick your latitude's column, read the month: the number is how many times the object's height its noon shadow stretches.
- Multiply any height by the ratio - a 20-foot wall at 2.0 in November throws a 40-foot noon shadow across the yard it shaded in May at 8 feet.
- Design with the December column, not the June one: the winter ratio is the one that decides whether the bed, the panels or the patio see the low sun at all.
Frequently asked questions
How long is a shadow at noon?
At noon the sun is at its daily highest, so the shadow is at its daily shortest: height divided by the tangent of the sun's noon altitude. On the equinox at 45°N that altitude is exactly 45°, so the shadow exactly equals the object's height - the ratio is 1.00. In June at the same latitude the ratio drops near 0.5; in December it climbs past 2.5.
Why are winter shadows so long?
Because the winter sun crosses the sky low: at 40°N its noon altitude is about 27° at the December solstice versus 73° in June, and shadow length grows as the tangent of the complementary angle - a low sun stretches shadows disproportionately. The December noon shadow at 40°N is roughly double the object's height, and at 50°N it passes three times - the same low-sun geometry that makes winter mornings and evenings feel dark in every direction.
What is the shadow rule for solar panels and gardens?
Multiply the obstacle's height by the December ratio of your latitude - not the June one - to find how far its noon shadow reaches in the season when sun is scarce. A two-story roofline (about 20 feet) at 40°N reaches 40 feet in December but only 6 in June: the garden bed that worked in May is in that shadow by October, and the panel row inside it loses the winter kilowatt-hours that matter most.
When is my shadow equal to my height?
On the equinoxes (late March and late September) if you live at 45°N - anywhere the noon sun sits 45° high, the shadow ratio is exactly 1:1. At other latitudes the 1:1 day shifts: the closer you are to the tropics, the more of the year your noon shadow runs shorter than you, because the noon sun climbs higher than 45° for more months.
How do I measure sun exposure for a garden without instruments?
Use the December column and a stick: on a midwinter noon, lay out the shadow of any obstacle - its height times the table ratio - and everything inside that line gets winter's weakest sun. The summer picture is easy (almost everything is lit); the winter map is the one that kills marginal plants and surprises panel owners, and one noon with a tape measure draws it exactly.