Every European city has a season when the sun cannot help you

Vitamin D synthesis depends on UVB, the shortest and most easily scattered part of the light that reaches the ground. It only arrives in useful quantities when the sun sits high overhead, because at lower angles the light travels through enough atmosphere that the UVB is absorbed before it gets to you. Heat still comes through. So does the glare. Neither has anything to do with the reaction happening in your skin.

The practical threshold most people can check without instruments is the shadow rule: when your shadow is shorter than you are, the sun is above 45 degrees, and that is where synthesis is quickest. Between 30 and 45 degrees it still works and simply takes longer outdoors, and below about 30 degrees it effectively stops, which is the state usually called vitamin D winter.

We calculated the maximum solar elevation for every day of the year in 38 European cities. Not one of them escapes a vitamin D winter, including Málaga at the southern edge of the continent.

38 cities, one year, by latitude

Each bar is a full calendar year, read left to right as the days the sun is high enough for synthesis to be quick, the days it still works but takes longer, and the days it cannot help at all.

When does vitamin D winter start in your city?

Two different seasons are worth keeping apart. The first is the stretch when the midday sun clears 45 degrees and synthesis is quickest, which in London runs from 7 April to 5 September, in Paris from 31 March to 12 September, in Berlin and Amsterdam from 9 April to 3 September, in Barcelona from 12 March to 2 October, and in Stockholm for barely three and a half months, from 29 April to 14 August.

The second is vitamin D winter itself, the deeper part of the year below 30 degrees where synthesis effectively stops. London spends 135 days there, from roughly the middle of October until the end of February. Berlin spends 140, Amsterdam 139 and Paris 120. Stockholm spends 175, which is close to half the year, and Reykjavík 199. Even Barcelona, which many people think of as a winter sun destination, closes for 72 days, and Málaga, the sunniest city in the set, still shuts down for 13 days around the December solstice.

Three things the numbers change

Moving south helps less than people expect. Madrid gets 210 days above 45 degrees against London's 152. That is a real difference, but it is 38 percent rather than the doubling most people imagine when they relocate for the light, and Madrid still spends 64 days a year in vitamin D winter.

The useful hours are not simply the bright ones. Even in the far south the sun clears 45 degrees for under seven hours on the best day of the year, and in Paris on the summer solstice it is 6.3 hours, falling roughly between nine in the morning and half past three. You do not need to spend all of that outside, because a short exposure is enough and gets shorter the higher the sun climbs, but you do need to be outside somewhere inside it, and that is precisely the stretch most people spend indoors.

Latitude sets the calendar, not the weather. Barcelona and Rome sit within half a degree of each other and get 205 and 202 days respectively. Clouds change how it feels; they do not change when the sun is high enough for the reaction to run.

Questions the data answers

How this was calculated

For each city we computed the sun's maximum elevation on every day of the year, which occurs at solar noon and equals 90 degrees minus the absolute difference between the city's latitude and the solar declination for that date. Declination was derived from a standard astronomical approximation accurate to within about 0.2 degrees. The solstice window was solved from the same relationship, giving the hours per day the sun exceeds 45 degrees.

Both thresholds are borrowed. The 45 degree shadow rule began life as a sun protection signal, the point at which your shadow becomes shorter than your height and the advice is to seek shade. The modern version of that advice is to cover up once the UV index passes 2, which on a clear day corresponds roughly to the sun clearing 30 degrees. We have repurposed both as synthesis thresholds because the same geometry governs both, and because the tension between them is the whole subject: the light that makes vitamin D is the same light that burns you.

What these figures deliberately do not measure is dose. Only a brief exposure is needed to produce a useful amount of vitamin D, the higher the sun sits the shorter that exposure becomes, and in every case it is well short of what would burn a sensible area of unprotected skin. So the solstice window column tells you when in the day to go outside rather than how long to stay there, and a city with a narrow daily window is not thereby short of opportunity on that day. What separates these cities is the number of days, which is what the index counts.

These are astronomical figures describing potential rather than status. They say when the sun is geometrically capable of driving synthesis, not how much any individual will produce, which also depends on skin tone, exposed surface area, altitude, cloud cover, ozone, air quality and sunscreen. People in Madrid are not thereby better supplied than people in London, since what anyone ends up with depends on how they behave inside that ambient light, and southern Europeans often test lower for exactly that reason. Glass blocks UVB entirely, so time spent behind a window counts as none of this.

As a cross-check, UK public health guidance, and discussion with Prof Webb at University of Manchester, puts the period when sunlight cannot supply vitamin D at roughly October to March. Our calculation gives London 135 days below 30 degrees and Manchester 145, which arrives in the same place from a different direction.