Sunset Direction: Why It Moves Through the Year

The sun sets due west on two days a year, at the equinoxes. Every other day it sets somewhere else, and at high latitude the somewhere else is a long way off.

This is the part of sunset planning that catches people out. Timing is easy to look up; direction is not, and a viewpoint chosen in June can be facing the wrong part of the sky in December.

Reading a bearing

Compass bearings run clockwise from north: 0° is north, 90° east, 180° south, 270° west. A sunset at 300° is west-northwest; one at 240° is west-southwest.

Every row in the table shows the same pattern. In December the sun sets south of west; in June it sets north of west. The swing column is how far apart those two are.

Nairobi, almost on the equator, swings 47 degrees. London swings 79. Reykjavík swings far more still. The further from the equator you stand, the more the sunset point wanders.

Why it moves at all

The sun's position against the stars traces the ecliptic, tilted 23.4 degrees to the equator. Over a year its declination — its angular distance north or south of the celestial equator — runs from +23.4° at the June solstice to −23.4° at the December one.

Where it sets on your horizon follows from that declination and your latitude:

cos(sunset azimuth) = -sin(declination) / cos(latitude)

At the equator, cos(latitude) is 1 and the azimuth swings between roughly 66.6° and 113.4° either side of due west — a total of about 47 degrees, which is what the table shows for Nairobi.

As latitude increases, cos(latitude) shrinks, so the same declination range produces a larger azimuth swing. At 60 degrees the divisor is 0.5 and the swing roughly doubles. Beyond the Arctic Circle the equation stops having a solution for part of the year, because there is no sunset to have a bearing.

What it means for a viewpoint

A viewpoint is a fixed direction. The sun is not.

A west-facing beach works best at the equinoxes and is off by tens of degrees at the solstices. In Britain, a beach that has the sun setting over the water in March and September may have it setting over land in December.

A gap between buildings is the most demanding case. A city street aligned east-west catches the sun down its length only near the equinoxes, which is the whole basis of Manhattanhenge in New York and its equivalents elsewhere. New York's street grid is rotated about 29 degrees from true east-west, which is why its alignment dates fall in late May and mid-July rather than at the equinoxes.

A mountain silhouette is usually fine for a few weeks either side of a target date and then not, because the sun moves along the ridge and eventually off the end of it.

The practical version: check the bearing for the date you are actually going, not the date you scouted.

Sunrise moves too, in mirror

Sunrise bearings do the same thing on the eastern side of the sky. If the sun sets at 300° it rose at about 60°, reflected about the north-south line.

The two are not exactly symmetric, because the sun's declination changes over the course of a day, but for planning purposes the mirror rule is close enough: sunrise bearing ≈ 360° minus sunset bearing.

That relationship is one of the few genuinely measurable differences in the sunrise-versus-sunset argument: they happen on opposite sides of the sky, and at high latitude those sides are far apart.

How fast it moves

The rate is not constant. Declination changes fastest near the equinoxes and barely at all near the solstices, so the sunset point does the same.

Around the equinoxes at mid-latitudes, the sunset bearing moves roughly a third of a degree per day — about ten degrees a month, easily visible over a few weeks from a fixed window. Near the solstices it almost stops, which is what "solstice" means: sun-standing-still.

If you are trying to catch a specific alignment, the equinox periods give you a narrow window and the solstice periods give you weeks of near-identical geometry.

Finding your number

Every city page here shows tonight's sunset bearing in degrees with a compass label and a plain instruction — face west-northwest, and so on. The information-gain section states how far the bearing travels across the year for that specific city, and the extended monthly table gives the bearing for every day of the month, so you can see it move.

If you are planning a composition, that column is the one to read before you commit to a viewpoint.

The alignment events

Once you know the sunset bearing moves, a whole category of local phenomena makes sense.

Manhattanhenge is the best known. Manhattan's street grid runs about 29 degrees off true east-west, so the sun sets straight down the cross streets on two pairs of dates — around 28 May and 12 July — rather than at the equinoxes. Thousands of people stand in the middle of 42nd Street for it.

Every city with a regular grid has its own version on its own dates, determined entirely by the grid's rotation. Chicago, Toronto, Montreal and Baltimore all have them. So does any street, anywhere, that happens to point at the right bearing.

Neolithic alignments are the same idea built deliberately. Newgrange in Ireland is aligned on the December solstice sunrise; Stonehenge on the June solstice sunrise and the December solstice sunset. Both work because the solstice bearings are the two extremes of the annual swing, and therefore the only bearings the sun returns to reliably and holds for several days.

That is why solstice alignments are common in ancient monuments and equinox alignments are rarer: near the solstice the sunset point barely moves for a fortnight, so the alignment is forgiving. Near the equinox it moves a third of a degree a day, and a monument built to catch it would only work for a day or two.

Checking an alignment yourself

If you want to know when the sun will set down a particular street, or behind a particular peak:

1. Get the bearing of the target from where you will stand. A map with a bearing tool, or a compass corrected for magnetic declination, will do.
2. Look up the sunset bearing on the city page for candidate dates and find where it matches.
3. Remember there are usually two dates a year for any bearing between the solstice extremes — one as the sun moves north, one as it moves back.
4. Allow for the sun's size. Its disc is about half a degree across, so an alignment is good for roughly a day either side at mid-latitudes.

The extended monthly table on every city page has the bearing for each day of the month, which is enough to find both dates without any other tool.