The Equation of Time: Why a Sundial Runs Ahead of Your Clock in November and Behind It in February

A sundial looks simple, and then it disagrees with your watch. Even a perfect one, built carefully and placed in the middle of its time zone, will be fast in some months and slow in others. People often blame the sundial. The sundial is right. The clock is the one that makes a deliberate simplification.

This guide explains that gap, which has a name: the equation of time. It covers what the term means, the two causes behind it, the size of the gap through the year, and why early November is the date to remember. It ends with a short task in the Clock Dial.

Sun time and clock time

The U.S. Naval Observatory defines the equation of time as apparent solar time minus mean solar time. Those two terms carry the whole idea.

Apparent solar time is what a perfectly constructed and calibrated sundial reads. It follows the real Sun in the real sky. Mean solar time follows an imaginary Sun that moves at a constant rate along the celestial equator all year. Clocks are built on that steady average, because a mechanical or electric clock cannot speed up and slow down with the seasons. The Naval Observatory adds that this imaginary Sun is never more than about 4 degrees east or west of the real one.

NOAA's solar glossary gives a compact version: the equation of time accounts for changes in the time of solar noon for a given location over the course of a year. In practice, that means the moment of solar noon drifts against the clock as the months pass.

How large is the drift? The Naval Observatory says the Sun's apparent rate across the sky changes by only about 0.03 percent, yet the accumulated difference can reach as much as 16 minutes. NIST gives the same figure.

Why the Sun is not a steady clock

The Naval Observatory explains that the Sun's daily motion has two parts. Earth's rotation carries the Sun across the sky at 15.04 degrees per hour, a rate that is constant to within milliseconds per day. Earth's trip around the Sun adds a much slower drift of about 1 degree per day in the opposite direction, and that part can vary by as much as 12 percent over a year. The equation of time comes entirely from that second part. Two things make it vary.

1. The tilt of Earth's axis. Earth's axis is tilted by 23.4 degrees. Because of this, the Sun's daily path climbs higher in summer and sinks lower in winter. The Sun's east-west rate also speeds up and slows down as its track changes. The Naval Observatory says this part of the equation is zero at the equinoxes and solstices and can reach plus or minus 10 minutes at other times. If the axis were perpendicular to the orbit, it would vanish, and so would our seasons. The guide on axial tilt tells that side of the story.

2. The oval shape of the orbit. Earth's orbit is almost a circle but not quite. The Naval Observatory gives its eccentricity as 0.0167. Earth is closest to the Sun in early January and farthest in early July, and it moves fastest at the closest point. As a result the Sun's total rate across the sky is slowest in December and January and fastest in June and July. The largest offsets from this effect arrive in early April (minus 7.5 minutes) and early October (plus 7.5 minutes). The guide on perihelion and aphelion covers the January and July dates.

The Naval Observatory states that the two effects have similar sizes, so neither one is the main cause. The bars show each part's own largest size. The two parts are not strictly additive, because the tilt effect modulates the orbit effect, so the bars are not meant to sum to 16.

The year at a glance

NOAA's tide glossary describes the whole year in words. Read "mean time ahead of apparent time" as "the clock is ahead of the sundial."

The Naval Observatory fits the middle row: at the end of July the equation of time is about minus 7 minutes, so a sundial reads about 7 minutes behind local mean solar time.

Official pages round the peak in different ways. The Naval Observatory and NIST both say as much as 16 minutes. NOAA's tide glossary says nearly 17 minutes in early November and about 15 minutes near mid-February. NASA Goddard says at most about 15 minutes. This guide uses about 16 minutes as the working value.

Sign conventions vary too. The Naval Observatory subtracts mean time from apparent time, so a plus sign means the sundial is ahead. NOAA's tide glossary skips signs and says which kind of time is ahead. This guide uses ahead and behind for the same reason.

Where early November comes from

The Naval Observatory pages used here give no single line saying the peak falls on one exact day. They give two clues that point to early November.

The first clue: around November 3, the clock effect changes sign and the Sun begins to run later each day by the clock. In the language of the curve, a sign change like that marks the top of the peak.

The second clue comes from the equator. There the Sun's daily track above the horizon is always exactly half a circle, so the clock effect alone decides when sunrise and sunset occur. The Naval Observatory says that at the equator the earliest sunset falls around November 2 and the latest sunrise around February 11. The Sun runs furthest ahead of the clock when sunset comes earliest. It runs furthest behind when sunrise comes latest. The same page says the total variation at the equator is only about half an hour, which fits a swing from about 15 minutes behind to about 16 minutes ahead.

The equation of time also moves the date of the earliest sunset. The Naval Observatory says the effect pushes sunrises and sunsets later each day from early November until mid-February. At 40 degrees north, the earliest sunset therefore comes around December 8, before the winter solstice, and the latest sunrise around January 5.

After the November peak, the gap shrinks. The Naval Observatory notes that around late December the Sun is at its slowest rate, with each solar day almost half a minute longer than 24 hours. Each day the sundial loses a little ground against the clock.

Reading a sundial with the correction

To turn a sundial reading into clock time, the sundial's own reading needs three corrections.

1. The equation of time. In early November a perfect sundial is about 16 minutes ahead. On a zone's central meridian in standard time, when it reads 12:00 the clock reads about 11:44.
2. Your longitude. The Naval Observatory gives a rule of 4 minutes for each degree of longitude away from the zone's defining meridian.
3. Daylight saving time. NASA Goddard notes that a sundial is one hour off in summer, when clocks are reset.

The Naval Observatory adds that on the central meridian of a time zone, local mean solar time equals civil time to within 0.9 second. Once daylight time is off, the equation of time is the only gap left. Anywhere else a constant offset from longitude also applies.

Eye safety. Read the shadow, not the Sun. NASA says it is not safe to look directly at the Sun without specialized eye protection for solar viewing, and that regular sunglasses, no matter how dark, are not safe. The shadow on the dial gives you the time. NASA's Eclipse Viewing Safety page, listed with this guide's sources, has the full guidance.

Common mistakes

• Blaming the sundial. A well-made sundial shows apparent solar time. The difference from the clock is the equation of time, not an error.
• Mixing it up with time zones or daylight saving. Those are fixed offsets of 4 minutes per degree and 1 hour. The equation of time changes with the date.
• Thinking it adds up year after year. The Naval Observatory says the curve is essentially the same from year to year and for all longitudes.
• Assuming the sundial is always fast or always slow. By NOAA's description it flips from behind to ahead and back again through the year.
• Crowning one cause. The tilt and the oval orbit have similar sizes, according to the Naval Observatory.
• Mixing up plus and minus. Sources use opposite sign conventions. Check the wording before you trust the sign.
• Looking at the Sun to read the dial. Use the shadow. NASA says looking at the Sun without proper solar eye protection is not safe.

Try it in the instrument

Open the Clock Dial and set the sky to the date when a sundial runs furthest ahead of the clock. The target is early November, around November 3, when the gap is about 16 minutes.

The relation is easy to hold on to. From early September to late December the sundial is ahead of the clock, and NOAA puts the peak of that stretch in the early part of November. The Naval Observatory backs it up with its turning point around November 3 and its earliest equatorial sunset around November 2. That peak is the biggest gap of the year, as much as 16 minutes. The dial is a simplified model with a window of accepted answers, so early November is the idea to land on. Mid-February is the opposite peak, with the sundial about 15 minutes behind.

Questions people ask

What is the equation of time in plain words?

It is the gap between sundial time and clock time on a given day. The Naval Observatory defines it as apparent solar time minus mean solar time. The gap changes with the date and reaches as much as about 16 minutes.

When is a sundial furthest ahead and furthest behind?

Furthest ahead in early November, by about 16 minutes. Furthest behind near mid-February, by about 15 minutes in NOAA's wording. The Naval Observatory points to November 3 and to February 11 through its dates for the equator's earliest sunset and latest sunrise.

Does the equation of time change from year to year?

Hardly. The Naval Observatory says the plot is essentially the same from year to year and for all longitudes. A table of daily values appears in its annual booklet, Astronomical Phenomena.

Why is the earliest sunset before the winter solstice?

Two effects compete. The length of daylight is shortest on the solstice, but the equation of time pushes sunrises and sunsets later each day from early November until mid-February. The Naval Observatory says that moves the earliest sunset ahead of the solstice. See the winter solstice guide for the daylight side.

What is the analemma?

It is the figure-eight you get by plotting the equation of time against the Sun's noon height. The Naval Observatory describes it as the pattern of Sun images you would record with a fixed camera at noon mean solar time on every clear day of the year.

Sources

• The Equation of Time, U.S. Naval Observatory, Astronomical Applications Department. https://aa.usno.navy.mil/faq/eqtime. Opened November 9, 2026.
• Sunrise and Sunset Times Near the Solstices, U.S. Naval Observatory, Astronomical Applications Department. https://aa.usno.navy.mil/faq/rs_solstices. Opened November 9, 2026.
• Tides and Currents Glossary, NOAA Tides & Currents. https://tidesandcurrents.noaa.gov/glossary.html. Opened November 10, 2026.
• Solar Calculator Glossary, NOAA Global Monitoring Laboratory. https://gml.noaa.gov/grad/solcalc/glossary.html. Opened November 10, 2026.
• Time and Frequency from A to Z, S to So, NIST Time and Frequency Division. https://www.nist.gov/pml/time-and-frequency-division/popular-links/time-frequency-z/time-and-frequency-z-s-so. Opened November 10, 2026.
• The Sundial, NASA Goddard Space Flight Center (ISTP historical pages, Dr. David P. Stern). https://pwg.gsfc.nasa.gov/stargaze/Sundial.htm. Opened November 9, 2026.
• Eclipse Viewing Safety - NASA Science, NASA Science. https://science.nasa.gov/eclipses/safety/. Opened November 10, 2026.

We opened each source ourselves on the date shown. The drawings are our own and were checked against the numbers in these sources.

Read next

• Solar NoonSolar noon is the moment the Sun crosses the north-south line above your head and reaches its highest point of the day.
• The Sidereal Day and the Solar DayA sidereal day is one turn of Earth measured against the stars, about 23 hours 56 minutes 4 seconds.