Firdaria
Calculator

Firdaria, the Latin name for the Arabic fardārāt (singular fardār), is a medieval time-lord technique. A life passes from one ruler to the next in a fixed order, each ruling for a fixed number of years: the Sun 10, Venus 8, Mercury 13, the Moon 9, Saturn 11, Jupiter 12, Mars 7, the North Node 3 and the South Node 2. The nine add up to 75 years, after which the round begins again.

The order depends on sect. A person born by day starts with the Sun and a person born by night with the Moon; after that the planets follow the order of their spheres, each one handing over to the planet below it: Saturn, Jupiter, Mars, the Sun, Venus, Mercury, the Moon, and back to Saturn. Inside each planet's period the same order deals out seven equal sub-periods. The period's own planet takes the first seventh, and each of the others then shares the rule in turn.

The fullest early account is in Abu Ma'shar's On the Revolutions of the Years of Nativities (ninth century), a handbook of the year-by-year techniques: annual profections, the solar revolution and the firdaria among them. Abu Ma'shar, and al-Dāmaghānī after him, quote the Persian astrologer al-Andarzaghar on how the periods run, which is why the technique is called Persian. Al-Qabīsī's Introduction to Astrology carried a short summary into Latin, and Guido Bonatti's Book of Astronomy made it a standard part of European practice in the thirteenth century.

The period's planet is read like the lord of a profection year. Its condition in your birth chart (sign, house, aspects, and whether it belongs to the chart's sect) sets the tone of the years it rules, and the sub-period lord brings its own matters into them for a year or two at a time.

These are the steps the calculation follows. Ephemeris files and time zone handling are shared by all our tools and described on the methodology page.

1. Birth moment. Your clock time becomes Universal Time through the IANA time zone database, daylight saving included.
2. Day or night. The Swiss Ephemeris gives the Sun's longitude and the true Ascendant for that moment. The chart is diurnal when the Sun is above the horizon, in the half of the zodiac from the Descendant up through the Midheaven to the Ascendant, and nocturnal otherwise. The sect calculator shows the same test with the Sun's altitude.
3. Order. By day: Sun, Venus, Mercury, Moon, Saturn, Jupiter, Mars, North Node, South Node. By night: Moon, Saturn, Jupiter, Mars, then either the two nodes followed by the Sun, Venus and Mercury (the default) or the Sun, Venus and Mercury followed by the nodes (Abu Ma'shar, chosen in the form).
4. Dates. A period of n years ends on the n-th birthday after it starts, at your birth time in your birthplace's time zone. Every major period therefore starts on a birthday. Someone born on February 29 changes period on February 28 in common years.
5. Sub-periods. Each planet's period is cut into seven equal parts, to the second. The first goes to the period's planet and the rest follow the order of the spheres downward: in the Sun's period, the Sun, Venus, Mercury, the Moon, Saturn, Jupiter and Mars. The nodes' periods are not divided: Abu Ma'shar says the planets do not share with them, because the nodes have no signs of their own.
6. Range. Two full rounds, 150 years, so the second round is there for anyone past 75.
7. “Now”. The current period and sub-period are found by comparing instants in Universal Time, and every date is printed as the calendar date in your birthplace, so a period that begins at 7:24 PM in Honolulu shows that day's date, not the next day's in Greenwich.

The ages each lord covers in the first round, for a day chart and for a night chart under both placements of the nodes. Add 75 for the second round.

Sub-period lengths are averages, a seventh of the period in calendar years of 365.2425 days; the calculator divides the exact span between the two birthdays, so they vary by a fraction of a day with the leap years inside it. A seventh rarely comes out in whole months: Mercury's 13 years give sub-periods of about 678.3 days, the Moon's 9 years 469.6 days, and only Mars's 7 years give almost exactly a year each.

In a day chart the sources agree: the nodes follow Mars and close the round at 70 to 75. For a night chart there are two orders in use, and they differ from age 39 to 75.

• Nodes after Mars: Moon, Saturn, Jupiter, Mars, North Node, South Node, Sun, Venus, Mercury. This comes from Bonatti, who says the night sequence runs in all respects like the day one, which readers take to mean the nodes keep their place after Mars. Robert Zoller, who translated Bonatti, taught this order, and it is what this calculator has always used. It remains the default.
• Nodes last: Moon, Saturn, Jupiter, Mars, Sun, Venus, Mercury, North Node, South Node. Abu Ma'shar states it outright near the end of his treatment of the fardārs: the nodes take over after Mars in a day chart and after Mercury in a night chart, in either case when the native enters the 71st year. Al-Dāmaghānī quotes al-Andarzaghar saying the same.

Steven Birchfield's paper The Fardārāt in Nativities sets the two texts side by side and argues that Bonatti was working from al-Qabīsī's short summary, which never says where the nodes go at night, since Abu Ma'shar's book had not yet been translated into Latin. Practitioners still use both, and the choice is yours: the form's “nodes in a night chart” setting switches between them.

Barack Obama's birth certificate gives 7:24 PM, August 4, 1961, in Honolulu: 05:24 UTC on August 5, 1961. The Sun had set; it stood 4.21° below the horizon, so the chart is nocturnal and the Moon takes the first period. The two night orders give these major periods:

Each period starts at 7:24 PM on his birthday in Honolulu time; in Universal Time that is already 5:24 AM the next day, which is why a calculator working in UTC dates would show August 5. The orders agree for his first 39 years and part at August 4, 2000, when the default order turns to the North Node and Abu Ma'shar's to the Sun.

Sub-periods of the Moon

His first period, the Moon's 9 years, divides into seven of 469.57 days each, about 1 year and 3½ months, handed down the order of the spheres from the Moon:

The periods on his 60th birthday

Setting the date to August 4, 2021, the evening he turned 60, shows how far apart the two orders can be:

• Nodes after Mars: the Venus period (ages 54–62), in its 6th sub-period, Venus–Mars, from April 21, 2021 to June 13, 2022. Mercury follows on August 4, 2023.
• Nodes last: the Mercury period (ages 57–70), in its 2nd sub-period, Mercury–Moon, from June 13, 2020 to April 22, 2022. The North Node follows on August 4, 2031.

The example shows the arithmetic only and makes no claim about his life in those years. To check the API, the generator script rebuilt all 232 period and sub-period boundaries of both orders with its own code, from birthdays and sevenths, and none differs by more than a second.

Some programs count each period as so many years of 365.25 days from the moment of birth. Four years of that count make one leap-year cycle, so the boundaries wander a quarter of a day a year around the birthday and come back every fourth year. For Obama the 10-year mark of that count falls 12 hours after his 10th birthday, on the morning of the next day in Honolulu, and 4 of the 9 boundaries in his first round land on a different date from the birthday. Across 1,000 sample birth moments between 1900 and 2000, 769 had at least one period starting a day early or late.

The calculator starts every major period on the birthday itself, at the birth time. The texts count the periods in years of age, and a birthday is where a year of age ends. Sub-periods are then exact sevenths of the span between two birthdays.

The notes below give each lord's traditional meanings and what to look at in the birth chart when its period begins. The medieval authors judge a period by how well placed its lord is, so the same Saturn period reads differently in a day chart with Saturn in its own sign than in a night chart with Saturn in its fall.

• Abu Ma'shar, On the Revolutions of the Years of Nativities, translated from the Arabic by Benjamin N. Dykes in Persian Nativities IV (Cazimi Press, 2019): the period lengths, the day and night orders, the seven sub-periods, and the nodes after Mercury in a night chart.
• Al-Qabīsī, The Introduction to Astrology, edited and translated by Charles Burnett, Keiji Yamamoto and Michio Yano (Warburg Institute, 2004): the short account that reached Latin readers.
• Guido Bonatti, Book of Astronomy (thirteenth century), the treatise on nativities: the source of the nodes-after-Mars order for night charts.
• Steven Birchfield, The Fardārāt in Nativities (2005, revised 2020): quotes Abu Ma'shar, al-Dāmaghānī, al-Qabīsī and Bonatti side by side and tabulates both night orders.
• Our methodology page: the Swiss Ephemeris files deployed (1800–2399), time zones and the house systems.