time, calendar, and cosmology
How did ancient Hindu astronomers calculate the length of the year, and how accurate were they?
What they were trying to measure
Hindu astronomers wanted to know exactly how long the Earth takes to complete one journey around the sun. They focused on the sidereal year — the time it takes for the sun to return to the same position against the background stars. Getting this right mattered for the calendar, for religious festivals, and for predicting eclipses.
How they worked it out
They had no telescopes. Instead, they used long, careful observation of the sky over many years, combined with detailed mathematics. They tracked the positions of the sun, moon, and planets using a system of cycles and epicycles — mathematical circles within circles that described how celestial bodies appeared to move. One key idea was the shighroccha, a point used to correct for the varying speed of a planet in its path. By combining these observations with arithmetic and algebra, they built precise models of the sky.
The numbers they reached
The results were striking. The figure given in the Aryabhatiya works out to 365 days, 6 hours, 12 minutes, and 30 seconds. The modern accepted value for the sidereal year is 365 days, 6 hours, 9 minutes, and 10 seconds. That is a difference of just over three minutes. The Surya Siddhanta, another major text in this tradition, gives its own close figure. Brahmagupta, working later, refined these calculations further in his Brahmasphutasiddhanta. Each of these texts shows a tradition of checking and improving on earlier work.
How accurate is that, really?
A three-minute error over a full year is remarkably small. Over centuries, small errors in the year length add up and shift the calendar, so precision mattered. By comparison, many other ancient traditions used rougher estimates. The Hindu astronomical tradition stands out for how close it got using only naked-eye observation and mathematics. Modern astronomy confirms these figures using instruments and methods that did not exist then.
Why it still matters
These calculations are the foundation of the traditional Hindu calendar, the Panchanga, which is still used today to set the dates of festivals, auspicious days, and religious observances. The tradition of precise astronomical thinking also fed into mathematics more broadly. The work done in this period is now recognized as a serious contribution to the history of science worldwide.