As per the Indian Hindu Calendar, Tithi (also spelled Thithi) is the lunar date. Tithi is one of the most important aspect of the Indian Almanac or the Panchang and therefore many Hindu festivals and ceremonies are based on Tithi Calendar. A lunar calendar is based on the moon’s rotation around the Earth. A tithi is the time taken for the longitudinal angle between the moon and the sun to increase by 12°. A lunar month consists of 30 tithis, whose start time and duration (19 to 26 hours) vary.
Tithi is also considered as the first phase or portion among the 16 phases of the Moon. The 15 days(First half of the Lunar Month), commencing from Amavasya (the last day of the dark half of a lunar month i.e. no moon or new moon day) to Pournima (Full moon), are called the Tithis of the Shukla-Paksha (Waxing phase) and the days commencing from Pournima (Full Moon day) to Amavasya (New Moon day) are called Krishna Paksha (the Waning phase). There are 30 Tithis in each lunar mont.
For example, at new moon (amavasya) the sun and the moon are separated by zero degrees. As they begin to separate the first tithi begins when the sun and the moon have separated by 12 degrees. The moon is now a tiny almost imperceptable sliver. The second tithi begins when they are separated by 24 degrees. The sliver is slightly larger. The third tithi begins when they have separated by 36 degrees. The digit of the moon is now clearly visible. And so it goes until the sun and moon have separated by 180 degrees. This tithi is called full moon, purnima. These first 15 tithis or phases of the moon make up the waxing phases of the moon which in Sanskrit this is called the sukla-paksa. This is the bright side of the lunar month. After purnima, full moon, the tithi begins again counting from one as the longitudanal separation between the sun and the moon decreases back to zero. This is called the waning phase of the moon or in Sanskrit, the krsna-paksa or dark side of the lunar month.
The tithis are sequentially numbered from both the points of the new moon as well as the full moon. In this way, the sukla-paksa ,beginning with the new moon (amavasya), is followed by the first tithi, then the second tithi, the third tithi and so on up to the 14th tithi. There is no 15th tithi. Instead, this tithi is called full moon (purnima). After the full moon, the waning phase (krsna-paksa) again begins with the first tithi, the second tithi, the third tithi and so on up to the fourteenth tithi followed by the new moon (amavasya). Afterwards the cycle repeats itself. In this way thirty tithis make up a lunar month, which is known as a masa or month. Some parts of India begin the month from the full moon whereas other parts begin the month from the new moon. Today, the lunar calendar is still in use throughout the world for Hindu religious purposes.
One of the greatest points of confusion between Hindu festival dates and the modern solar calendar is that the solar day begins at midnight whereas the lunartithi can begin at anytime of the solar day. For practical purposes, however, the tithi that is current at sunrise is taken as the prevailing tithi for the day.
Another aspect of the lunar calendar is that its twelve months based on the lunar days (tithis) contain about 354 days. Just like, every 4th year an extra day is added on the solar calendar to make up for the discrepancy in the earth’s orbit around the sun (leap year system), an extra month is added to the lunar calendar every 30 months. This leap-month (adika-masa) is generally inserted after the months of Asadha or Shravana and is called either a second Asadha or Shravana. Thus every second or third year contains 13 months in the lunar calendar. This of course contributes considerably to differences between the lunar and solar calendars. The consequences of these differences makes it hard to reconcile the dates from one calendar to the other without intricate calculations, especially in deciding the dates of various festivals. Your Lala Ramswaroop Ramnarayan Panchang serves the purpose of connecting the lunar calendar dates with that of solar calendar dates.