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How Accurate Are Calendars?

The Julian calendar was abolished because it did not reflect the length of a year on Earth accurately. Today's Gregorian calendar does a better job, but is there such a thing as a perfect calendar?

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The time it takes Earth to orbit the Sun defines the length of a year.


A Year Is Not 365 Days Long

The length of a year on Earth is defined by the time it takes our planet to complete a full orbit around the Sun.

Solar calendar systems, such as the modern-day Gregorian calendar, are designed to reflect the duration of a tropical year—also called a solar year, astronomical year, or equinoctial year—as accurately as possible. This is the duration of a full seasonal cycle, for example, from one equinox to the next. A tropical year is approximately 365.242189 days long on average, though its length changes slightly over time.

Because a common year has 365 days in today's Gregorian calendar, a leap day is regularly added to bring it in sync with the tropical year. Without leap days, our calendar would be off by 1 day approximately every 4 years, causing the astronomical seasons to occur at an increasingly later date as time goes by. In less than 50 years, the March equinox would be in April and the June solstice would occur in July.

Is There A Perfect Calendar?

The simple answer is no. None of the calendar systems currently in use around the world perfectly reflect the length of a tropical year. However, there are calendar systems that are more accurate than the Gregorian calendar we use today.

The table shows how accurately the different systems reflect the length of a tropical year, sorted from most to least accurate. Calendars that are designed to reflect time spans other than the tropical year are not listed. This includes the Islamic, Buddhist, and Hindu calendar systems.

Calendar Accuracy Comparison

CalendarIntroducedAverage Year LengthApproximate Error
Persian calendar2nd millennium BCE365.2421986 daysLess than 1 sec/year (1 day in 110,000 years)
Revised Julian calendar1923 CE365.242222 days2 sec/year (1 day in 31,250 years)
Mayan calendar~2000 BCE365.242036 days13 sec/year (1 day in 6500 years)
Gregorian calendar1582 CE365.2425 days27 sec/year (1 day in 3236 years)
Jewish calendar9th century CE365.246822 days7 min/year (1 day in 216 years)
Julian calendar45 BCE365.25 days11 min/year (1 day in 128 years)
Coptic calendar25 BCE365.25 days11 min/year (1 day in 128 years)
365-day calendar
(no leap years)*
-365 days6 hours/year (1 day in 4 years)

* There is no 365-day calendar system currently in use for civil purposes. Past examples include the ancient civil Egyptian calendar, the Maya Haab' calendar, and the Aztec Xiuhpohualli calendar.

The Modern-Day Calendar and Its Variants

The Gregorian calendar is the internationally used calendar system. It is derived from the Julian calendar developed in ancient Rome.

The Julian Calendar

In the Julian calendar, a leap day is added every four years without exception, so an average Julian year is 365.25 days long. The difference between the tropical and the Julian year is about 11 minutes per year, amounting to an error of 1 day every 128 years. Because of this inaccuracy, the Julian calendar was eventually replaced by the Gregorian calendar.

The Gregorian Calendar

Today's Gregorian calendar uses more elaborate leap year rules, making it far more accurate. However, it is not perfect either. Compared to the tropical year, it is 27 seconds too long, so it is off by 1 day every 3236 years.

The Revised Julian Calendar

This calendar system, an enhanced variant of the ancient Julian calendar, uses even more complex rules to determine when a leap day is to be added. With an error of only about 2 seconds per year or 1 day in 31,250, it is roughly 10 times more accurate than today's Gregorian calendar and one of the most accurate calendar systems ever devised.

Topics: Calendar, Leap Year