Horas de Luz por Latitude

Daylight hours: how latitude and day of year shape the length of the day

How long daylight lasts at any spot on Earth comes down to two things: where you are (latitude) and what day it is. The astronomical formula leans on the solar declination delta, the angle between the Sun and Earth's equatorial plane, which swings between -23.45 degrees and +23.45 degrees across the year. From that you get the hour angle H with cos(H) = -tan(latitude) * tan(delta), and daylight hours work out to 2H / 15. The equator hovers near 12 hours all year round. Sao Paulo (-23.5 degrees) gets roughly 14 hours at the December solstice and 10 at the June one. The poles are the extreme case: the Sun stays up for six months straight and stays below the horizon for the other six.

Example: take latitude -23.5 on day 172 (June 21, the winter solstice in the Southern Hemisphere). Solar declination is +23.45 degrees, which gives cos(H) = -tan(-23.5) * tan(23.45) ~= 0.188, so H ~= 79.2 degrees and daylight comes to ~= 10.56 hours.

Why it matters across disciplines

Photographers use it to plan the golden hour and blue hour. Farmers lean on it to predict vernalization windows and pick photoperiod-sensitive cultivars like soy, onion and wheat. In Brazil, architects check NBR 15575 to guarantee a minimum of sunlight reaching bedrooms. And tour operators can sell the Norwegian Midnight Sun only because, above the Arctic Circle, the Sun simply refuses to set from late May to late July.

FAQ

Does daylight equal sunrise-to-sunset? Not quite. The strict definition tracks the geometric center of the Sun, but real sunrise and sunset also factor in atmospheric refraction (~34 arcminutes) and the radius of the solar disk, and those add roughly 6 to 10 extra minutes.

Why is the equator not exactly 12 hours every day? Refraction and the solar disk nudge every latitude a little past 12 hours. At the equator that leaves the figure somewhere between 12h00 and 12h07.

What happens above the Arctic/Antarctic circles? Once |latitude| + |delta| passes 90 degrees, the formula breaks down and has no solution. That is when the Sun either never rises (polar night) or never sets (polar day).