Ahargaṇa — अहर्गण

Ahargaṇa (अहर्गण, literally "heap of days") is the count of civil days elapsed from a fixed epoch — usually the start of Kaliyuga at sunrise on Feb 18, 3102 BCE (Julian). Every Siddhāntic Pañcāṅga calculation begins by converting a calendar date into this single integer. This page walks through the arithmetic step by step.

Kaliyuga Epoch

Feb 18, 3102 BCE

Śaka Offset

+ 3179 years

Start Weekday

Friday

Mahāyuga

4,320,000 years

Pick a date to trace

Śaka Year

Lunar Month

Tithi (1–30)

Siddhānta / Method

Siddhāntic Constants (per Mahāyuga = 4,320,000 years)

Constant	Sūrya Siddhānta	Āryabhaṭīya	Paitāmaha
Civil Days	1,577,917,828	1,577,917,500	1,577,916,450
Solar Months	51,840,000	51,840,000	51,840,000
Intercalary Months	1,593,336	1,593,336	1,593,300
Lunar Days (Tithis)	1,603,000,080	1,603,000,080	1,602,999,000
Omitted Lunar Days	25,082,252	25,082,580	25,082,550

The tiny differences between siddhāntas reflect centuries of observational refinement. Sūrya Siddhānta's civil-day count (1,577,917,828) implies a sidereal year of ≈ 365.25875 days — remarkably close to the modern value of 365.25636.

Why BigInt arithmetic? Classical texts describe every step as an integer division with remainder (bhāgahāra). The numbers involved (Mahāyuga civil days ≈ 1.58 × 10⁹) exceed JavaScript's safe-integer threshold only modestly, but floating-point rounding of a single intermediate product can shift the final Ahargaṇa by a full day — and with it the weekday. This page uses BigInt throughout to match the exactness of the original algorithm.