What the Part of Fortune is
The Part of Fortune is the oldest and most widely used of the Arabic Parts (or "Lots") — calculated points derived from the positions of other bodies. It carries the symbolism of the Moon and the body: physical wellbeing, ease, prosperity and the area of life where things tend to come together and flow of their own accord.
In Hellenistic astrology it is the "Lot of the Moon" and forms a pair with its counterpart, the Part of Spirit (the "Lot of the Sun"). Together they describe the involuntary, embodied fortune of a life and its conscious, willed purpose.
How it is calculated
The Part of Fortune measures the same arc between the Sun and Moon, projected from the Ascendant. In a day chart (Sun above the horizon) it is Ascendant + Moon − Sun; in a night chart the formula reverses to Ascendant + Sun − Moon. Many modern programs ignore sect and always use the day formula — a real difference for night births, so it is worth checking which convention a chart uses.
The Part of Fortune in the chart
The sign and house of the Part of Fortune show where a person most naturally experiences ease, wellbeing and good fortune — the area of life that "works" with the least resistance. Its condition (aspects, ruler, and whether benefics or malefics are near) refines the reading. Traditional astrologers weigh the Part of Fortune heavily; modern practice often treats it as a supporting significator.