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 7 minutes

Equation of Time: How They Work and Three Stunning Models

By Tomas Renner

Equation of Time: How They Work and Three Stunning Models

Equation of time watches are few and far between. This unusual complication displays the difference between the length of a true solar day and the mean solar day. You’d be forgiven for not knowing exactly what that means, but we’ll explain it all below. There are some stunning luxury watches that features this rare complication, and we’d like to introduce you to three of them.

The 24-Hour System: Solar Days and Equation of Time

What we call a mean solar day above, also referred to as normal time, is actually a man-made average of a true solar day. A true solar day equals the time between the highest point of the sun from one day to the next. If you take an average across the year, this equates to roughly 24 hours in a day. True solar time almost always deviates from the mean solar day, however, except on four occasions throughout the year when the sun is at its highest point at 12 noon. These dates are December 25th, April 13th, June 13th, and September 1st. The largest deviation between the two times is around 15 minutes, which occurs on February 11th and November 3rd each year.

The basis of all time measurements is the solar day, or the time it takes the Earth to rotate on its axis in relation to the Sun. While we average this to 24 hours a day, we know it’s actually just 23 hours, 56 minutes, and a few seconds a day. We compensate for this deviation by adding an extra day every leap year.

As mentioned above, however, 23 hours and 56 minutes or 24 hours is just an average. The length of a solar day differs by as much as 15 minutes in February and November due to the titled rotational axis of the Earth and differences in speed during its elliptical orbit around the Sun. Sun dials depict actual solar time using the position of the Sun, but they only work if the sun is shining, of course. The invention of mechanical clocks that worked independently of the sun caused watchmakers to turn to the 24-hour system with time zones that we are familiar with today. After all, it wasn’t easy to display true solar time with a simple clockwork.

To put it more simply, if the sun is at its highest point in New York,the true solar time is 12 noon; however, the mean solar time determined by our 24-hour system may be 12:07 or 11:56, for example.

Equation of Time in Watchmaking

Ancient Greek astronomers and mathematicians had already noted that the length of days differed. They devised a formula to calculate these deviations, allowing them to determine the exact time of the sunrise and sunset each day.

These same calculations are still used by contemporary watchmakers to create equation of time complications. This is achieved with a parabolic-shaped disc linked to the normal time.

The difference between true solar time and mean solar time plots in a parabolic shape across the year (upper image), which is the same shape as the equation of time movement component (lower image).

Some watches display the true solar time with a second minute hand. One example of this is the Audemars Piguet Jules Audemars Equation of Time. Others feature a scale that displays the deviation from mean solar time. Such is the case with the Panerai Luminor GMT Equation of Time. Others still are able to display the exact sunrise and sunset times at a specific location and may be available with multiple discs representing different locations around the world.


Audemars Piguet Jules Audemars Equation of Time

Audemars Piguet Jules Audemars Equation of Time
Audemars Piguet Jules Audemars Equation of Time

The Audemars Piguet Jules Audemars Equation of Time is a true masterpiece of haute horlogerie as well as a stunning piece of jewelry.

The automatic AP 2120/2808 movement features an astronomical moon phase complication, a perpetual calendar, and a sunrise/sunset display for a specific longitude. Despite these complications, the movement is just 5.3 mm thick and boasts a power reserve of 40 hours. Each of the 425 pieces is elaborately hand finished. The sapphire crystal case back offers a view of the decorative movement at work.

The case measures 43 mm in diameter and stands 14 mm tall. It is available in 18-karat yellow, white, or pink gold. The original version comes with a black alligator leather strap. The dial is silvery white, though the pink gold version is also available with a black dial.

The watch has two hands that display the normal hours and minutes via Roman numerals. Solar time is displayed using a central hand with a sun on the tip and a minute scale around the dial edge between 4 and 10 o’clock. You will also find the name of the city that the equation of time is calculated for. You can find the sunrise and sunset times for this longitude on two subdials at 9 and 3 o’clock. Small hour and minute hands display the times using Roman numerals.

These displays are made possible by special cams unique to nearly every location on Earth. The manufacturer will even make custom bezels and cams upon request. You can also purchase a pre-loved watch from someone around the world and have it adjusted to suit your location.

Audemars Piguet Jules Audemars Equation of Time_2
Audemars Piguet Jules Audemars Equation of Time

The moon phase display is located at 12 o’clock. It is made of colored sapphire crystal and displays a clear dark blue night sky. The display is extremely precise thanks to its 135 notches as opposed to the standard 59. As a result, this moon phase display deviates by only 57 seconds per lunar cycle. In that same time, more simple moon phase complications deviate by roughly 45 minutes. Audemar Piguet’s moon phase won’t need recalibration until 2127, and even then it will only require adjustment via a small push-push in the case.

Around the edge of the moon phase display, you will find the names of the months. To the right is the leap year indicator. There is an additional subdial at 6 o’clock that displays the date and day of the week using two hands.

The dial has a spacious look despite its many features. Each subdial is either raised or embedded and the Roman numerals afford the dial a certain degree of simplicity and balance. The watch also comes with a crown and a discreet push-piece at 5 o’clock for correcting the calendar and moon phase display. The only downside to this watch is that it is only water resistant to 20 m (2 bar, 65 ft), which means it’s not even protected against splashes of water. Depending on the material, this model costs between 20,000 and 55,000 USD.

Breguet Classique Complications 3477 Equation

Breguet Perpetual Calendar Equation of Time 2
Breguet Perpetual Calendar Equation of Time


The Breguet Classique Complications 3477 is also known as the Breguet Equation of Time. Similar to the Jules Audemars, this watch has a sleek, classic look. It also boasts a perpetual calendar, but doesn’t have a moon phase display. The watch measures 36 mm across and will slip under any cuff with ease at just 10.5 mm tall. The silver-plated solid gold dial is clean and tidy.

Breguet also relies on Roman numerals for this watch. The days of the week are displayed using three-letter abbreviations at 12 o’clock. The equation of time display is located at the 2 o’clock position with a 45-degree subdial. It features a scale ranging from +15 to -15. The power reserve display at 11 o’clock balances the upper half of the dial. A month display is located more centrally.

The leap year display at 8 o’clock tells you whether it’s currently a leap year or not. In the year 2100, the complication will need to be corrected using the push-piece above the crown at 2 o’clock. As is typical for Breguet, you can find the model’s reference number on the right side of the dial next to the brand name. The day of the week is shown on a subdial with a hand at 6 o’clock.

The Breguet 3477 stands out with its high-quality materials and finishing. The dials feature blued hands and the case is made of either gold or platinum. The gold version has gold movement components and a gold guilloché rotor, while the platinum version features platinum components and a platinum rotor. You can view the beautiful Calibre 502 DPE in action through the sapphire crystal case back.

The movement runs at 18,000 vibrations per hour and has a 45-hour power reserve. The case is mounted on a black alligator leather strap with a fold-over clasp made of the same metal as the case. New, this model will set you back more than 167,000 USD. If you purchase a pre-owned model, expect to pay around 55,000 USD.

Panerai Luminor GMT Equation of Time

Panerai Luminor 1950 8 Days Acciaio
Panerai Luminor 1950 8 Days Equation of Time


The Luminor 1950 Equation of Time is a more robust, yet likewise attractive, alternative to the two previous dress watches. The satin-finished titanium case and matte brown or dark blue dial offer the watch an appealing degree of modesty.

The case measures in at 44 mm in diameter and features a crown guard that is typical for Italian Marines’ diving watches. There is also a 47-mm version available for more imposing wrists. The dial looks clean and balanced with luminous numerals at 3, 6, 9, and 12 o’clock. These are interrupted by line indices. The hands likewise feature luminous material. A central arrow-tipped hand displays a second time zone. There is also an AM/PM display integrated into the sleek small seconds scale on the left-hand side of the dial. 

In typical Panerai fashion, the deviation from solar time is displayed using a linear indicator above the 6 o’clock position. This is typically where Panerai’s power reserve indicator resides, but on this watch, it’s been moved to the reverse side, where it can be viewed beneath a sapphire crystal case back. This isn’t really a problem considering the manual P 2002/E caliber with three barrels has a power reserve of 8 days when fully wound. The dial design is rounded off by an easy-to-read date window at 5 o’clock.

While the Panerai offers fewer complications than the Audemars Piguet and Breguet watches, it stands out with its extra power reserve and water resistance to 200 m (20 bar, 656 ft). Not surprisingly, the less complicated watch is more affordable. The ref. PAM00670 with a blue dial and the PAM00656 with a brown dial cost around 22,000 USD new and 17,000 USD pre-owned.

Read more

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Grand Complications: Perpetual Calendar Watches

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About the Author

Tomas Renner

I'm Tomas, and I've been working for Chrono24 for several years now. The first watch I ever bought was a quartz Casio tool watch with an altimeter. When my father …

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