Why noon on the clock is not solar noon: the equation of time

Cause one: where you sit inside your zone

A time zone is an hour wide, 15 degrees of longitude, and the sun takes four minutes to cross each degree. Clock noon matches mean solar noon only on the zone's central meridian. Every degree east of it brings solar noon earlier by four minutes; every degree west pushes it later. On a zone's edges that is already half an hour either way, and real zones are often far wider than the ideal.

Madrid is the standard example. Spain keeps Central European Time, whose central meridian is 15 degrees east, but Madrid lies at 3.7 degrees west. That is 18.7 degrees, or about 75 minutes, west of where its clock belongs, so mean solar noon in Madrid falls at about 1:15 PM in winter. Urumqi, in China's far west, is about 32 degrees west of the central meridian of China's single zone, so its solar noon is around 2:10 PM all year.

Cause two: daylight saving

Daylight saving moves the clock forward an hour without moving the sun, so solar noon shifts to about 1 PM for everyone who observes it. Stack that on the longitude effect and Madrid's solar noon in summer lands around 2:15 PM, which is why the Spanish afternoon runs so late by the clock. Any sun page lists solar noon for today, and comparing it with 12:00 shows you the combined effect for that city.

Cause three: the sun itself runs fast and slow

Even on the central meridian, with no daylight saving, the sun is rarely overhead at exactly 12:00. The equation of time is the difference between apparent solar time, read from the real sun, and mean solar time, read from a fictitious sun that moves at a constant rate. It swings between about 16 minutes fast in early November and 14 minutes slow in mid-February, and passes through zero four times a year, around April 15, June 13, September 1 and December 25.

Two effects combine to produce it. Earth's orbit is slightly elliptical, so it moves faster along its orbit near perihelion in early January and slower in July, which makes the solar day a little longer or shorter than average. And the axial tilt means that the sun's motion along the ecliptic projects unevenly onto the equator, which is what clock time measures. One effect has a one-year cycle and the other a six-month cycle, and their sum is the lopsided curve astronomers call the analemma when plotted against the sun's declination.

What it changes in everyday life

• The earliest sunset is not on the shortest day. At 40 degrees north the earliest sunset comes around December 7, two weeks before the solstice, and the latest sunrise around January 4, two weeks after. The day is shortest on the solstice, but the equation of time drags both ends of it later through December. The sunrise and sunset tables show this directly.
• A sundial needs a correction table. A sundial reads apparent solar time. To get clock time you add the equation of time, then the longitude correction, then an hour for daylight saving if it applies. Old sundials often have the correction engraved on them.
• The sun panel on the globe shows it live. Click the sun on the home page globe and the panel reports the equation of time for the current moment alongside the subsolar point and season.

For the maths, the site uses the NOAA solar position equations, which compute the equation of time, declination and solar noon from the date alone and agree with almanac tables to within a minute or so. The methodology page documents them.

See it on the site

• Sun in MadridA city whose solar noon lands after 2 PM in summer, for the reasons above.
• Sunrise and sunset by citySolar noon for today beside sunrise, sunset and the twilight bands.
• Live globeClick the sun to read the current equation of time and subsolar point.