The equation of time is the changing difference between apparent solar time—the time shown by a sundial—and mean solar time, a smoothed time standard. In the United States Naval Observatory (USNO) convention, it is apparent solar time minus mean solar time: a positive value means the sundial is ahead of mean solar time; a negative value means it is behind.
What does “equation of time” mean?
Here, “equation” means a correction or difference, not a mathematical formula to solve for an unknown. A sundial follows the Sun’s actual apparent position across the sky. Mean solar time instead represents the Sun’s motion as if it progressed uniformly, giving a steadier basis for measuring time. The USNO states: “Technically, the Equation of Time is the difference apparent solar time minus mean solar time.” (United States Naval Observatory)
The sign can be easy to misread, so keep the subtraction order in mind: equation of time = apparent solar time − mean solar time. If the result is positive, the apparent Sun is ahead of the mean Sun; if negative, it is behind.
Why does it change during the year?
The apparent Sun does not keep exactly the same pace across the sky from day to day. Two aspects of Earth’s motion produce the changing offset:
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- Earth’s axial tilt: Earth’s axis is tilted by about 23.4°. The Sun appears to travel along the ecliptic, while mean solar motion is represented on the celestial equator. Projecting between those paths makes the Sun’s east–west apparent motion vary over the year.
- Earth’s elliptical orbit: Earth’s orbital speed changes as it travels around the Sun. That changes the apparent rate at which the Sun moves against the background of stars.
The USNO identifies both axial obliquity and orbital eccentricity as causes. (United States Naval Observatory) The small daily differences between the apparent Sun’s pace and the uniform mean pace build into a time offset that changes through the year.
How many minutes can the difference reach?
The accumulated difference can reach about 16 minutes, according to the USNO. Its example gives an equation-of-time value of about −7 minutes at the end of July: under the USNO sign convention, a sundial would then show apparent solar time about seven minutes behind local mean solar time. These are approximate, date-dependent values, not a correction that stays constant all year. (United States Naval Observatory)
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The USNO page plots an example for 2014 and says the curve is essentially similar from year to year. That is a dated illustration, not a current daily table. For a precise correction on a particular date, consult current ephemeris data.
Why is solar noon not necessarily 12 o’clock?
Solar noon is the moment the Sun crosses an observer’s meridian—the imaginary north–south line through that location. NOAA defines a mean solar day as the interval between successive solar noons averaged over the year, and describes the equation of time as accounting for the seasonal change in solar-noon time. (NOAA Global Monitoring Laboratory)
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But mean solar time is not the same as the time displayed by every civil clock. A time zone assigns a shared clock time across a region, while local mean solar time varies with longitude. The time-zone central meridian gives the closest correspondence to local mean time; locations east or west of it have an additional longitude offset. Daylight-saving time, where observed, shifts the civil clock as well. So the equation of time alone cannot convert every sundial reading directly into a wristwatch reading. (United States Naval Observatory)
What is an analemma?
An analemma is the familiar figure-eight-like pattern made by recording the Sun’s position at the same mean solar time each clear day over a year. It can also be understood as a graph of the equation of time against solar declination. The equation of time describes the east–west timing offset; declination describes the Sun’s changing north–south position through the seasons. (United States Naval Observatory) (NOAA Global Monitoring Laboratory)
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What does the equation of time mean for a sundial?
A sundial shows apparent solar time, so it will not track uniform clock time without correction. To compare its reading with a modern clock, account for the equation of time, the site’s longitude relative to its time-zone central meridian, and any daylight-saving adjustment. The specific correction depends on the date and location.
The equation of time also contributes to why the earliest sunset and latest sunrise do not fall exactly on the winter solstice, with corresponding shifts around the summer solstice. It is not the only factor: latitude and the Sun’s changing path also affect sunrise and sunset times. (NOAA Global Monitoring Laboratory)
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