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How the Hindu calendar reconciles lunar months with the solar year through the Adhika (extra) month
A lunar year of 12 months totals approximately 354 days — 11 days shorter than the 365-day solar year. Without correction, this gap accumulates: after just 3 years, festivals would shift by over a month. After 17 years, a monsoon festival would fall in winter. The Adhika Masa system prevents this seasonal drift by inserting an extra month every ~2.7 years, keeping the lunar calendar aligned with the solar seasons.
The classical criterion from the Surya Siddhanta: if no solar Sankranti (the Sun entering a new sidereal sign) occurs within a lunar month (New Moon to New Moon), that month is declared Adhika (intercalary). The Sun transits one zodiac sign in ~30.4 days, while a lunar month averages ~29.5 days. When these nearly overlap, the shorter lunar month can fit entirely within one solar sign — no Sankranti occurs, and the month becomes Adhika.
sign(NM_start) === sign(NM_end) → Adhika