A sundial and a clock rarely agree. Over the year the Sun runs up to about 16 minutes ahead of your clock in early November and about 14 minutes behind it in mid-February. That difference is called the equation of time, and it traces a figure-eight in the sky.

This is one of my favourite pieces of astronomy, because you can check it with nothing more than a stick in the ground, and because it exposes something we mostly forget: clock time is an invention.

Two kinds of day

There are two ways to measure a day.

  • Apparent solar time is what a sundial shows. Noon is the moment the Sun is at its highest point in the sky, on the line running due south (or north) of you.
  • Mean solar time is what your clock shows. Every day is exactly 24 hours, the average length of a solar day over the year.

If Earth's orbit were a perfect circle and its axis stood upright, the two would match all year. Neither is true, and the difference between them, sundial minus clock, is the equation of time.

Two reasons the Sun runs fast and slow

  1. Earth's orbit is an ellipse. Earth moves faster when it is nearer the Sun (in early January) and slower when it is further away (in early July). That changes how quickly the Sun appears to move across the sky day to day, so the solar day is a little longer or shorter than 24 hours at different times.
  2. Earth's axis is tilted. The Sun moves along the ecliptic, which is tilted against the celestial equator, and time is measured along the equator. Near the solstices the Sun's motion is mostly sideways and it "wastes" some of it when projected on the equator, while near the equinoxes it is more efficient. So the solar day varies again.

The two effects add together and cancel at different times of the year, giving the curve you see below.

The numbers

The US Naval Observatory has a page on the equation of time if you want the official tables. The rounded figures below are the commonly published ones, and the exact numbers differ by a few seconds between sources and from year to year. The largest values, about 16 minutes 33 seconds fast around 3 November and about 14 minutes slow in February, are widely quoted:

  • Around 11 February: the Sun runs behind the clock by roughly 14 minutes, the biggest lag.
  • Mid-April: the two agree, at around 15 April.
  • Mid-May: the Sun runs ahead by about 3.5 minutes.
  • Mid-June: the two agree again, around 13 June.
  • Late July: the Sun runs behind by about 6.5 minutes.
  • 1 September: the two agree, around 1 September.
  • Around 3 November: the Sun is ahead of the clock by roughly 16 minutes, the biggest lead.
  • Around 25 December: the two agree again.

So there are four days a year when a sundial and a clock agree, and two clear extremes.

The analemma

If you take a photograph of the Sun at exactly the same clock time every few days for a year, and stack the pictures, the Sun traces a figure-eight in the sky. That shape is called the analemma. Its height comes from the tilt of the axis, because the Sun is higher in summer and lower in winter. Its width comes from the equation of time, because the Sun is sometimes a bit east or west of where the clock says it should be.

Photographers have produced beautiful analemma images with a fixed camera and a year of patience. If you have a globe with a figure-eight printed on it in the Pacific, that is the analemma too.

Solar noon is not at 12:00

Two more things move solar noon away from 12:00 on your clock:

  • Time zones. A time zone is a wide band that uses one clock time. Across the band, solar noon differs by four minutes for every degree of longitude from the zone's central meridian.
  • Daylight saving. In summer, many countries put the clocks forward an hour, which pushes solar noon to around 13:00.

So in London in midsummer, solar noon is close to 13:00 and in western Spain it can be as late as 14:30, even though the clock says the same noon.

Try it yourself

Here is a very cheap experiment.

  1. Push a straight stick upright into flat ground, or use a garden cane in a pot.
  2. Every ten minutes around midday, mark the tip of the shadow.
  3. The shortest shadow is solar noon. Note the clock time.
  4. Do it again a month later.

You will see that the time of the shortest shadow shifts through the year, by exactly the amount the equation of time predicts. It takes ten minutes of attention a month, which is manageable even for a mind that gets bored quickly, because you are watching something change.

Why this matters to me

I built my Solar Blueprint around the Sun, not the Moon, and this is part of the reason. The Sun's rhythm is the one you can stand in and feel. Knowing that the Sun's own clock differs from the wall clock, by a known amount that you can calculate and check, is a small lesson in the difference between a map and the ground. It is the same lesson as why the zodiac drifted and the same as what a solstice really is.

For anyone with a mind that struggles with time, there is also something comforting in it: even the Sun is not on time by the clock. The ADHD MindFlow community is a good place to talk about time, and my post on time blindness tools has a few practical things to try.

Astronomy facts here are checked against the sources linked. Astrology is a way to reflect, not science, and it does not predict events.

Astrology is a way to reflect, not science, and it does not predict events. Astronomy facts here are checked against the sources linked. Read our sources, commercial disclosure and editorial approach.