What is actually being calculated
One number: the elongation, the angle between the Sun and the Moon as seen from Earth. At 0° the Moon sits in the same direction as the Sun and its lit face is turned away from us — a new moon. At 180° it is opposite the Sun and fully lit. Everything between is a fraction of that angle, and the illuminated part of the disc is a direct function of it.
So the phase is not a separate fact to be looked up. It is the same measurement the rest of this site uses, pointed at a different pair of bodies. The disc drawn above your birth date is not an illustration chosen from eight pictures: the bright limb is a semicircle and the terminator is an ellipse whose width is the cosine of that angle, which is exactly the shape the real Moon presents.
The eight phases
Eight names for a continuous quantity, each covering 45° of the cycle. Four of them — new, first quarter, full, last quarter — are instants that a whole day is named after; the other four are the stretches between. Each is set out at length here, with what it is astronomically and what it has traditionally been read as.
The cycle takes 29.53 days, which is where the month comes from and why a lunar calendar drifts against a solar one by eleven days a year. That drift is the entire reason the Chinese calendar needs a leap month, and why Easter moves.
Two moons together
Laying two birth moons side by side is a recent game rather than an old tradition, and it is worth being straight about that. From about 2022 a claim circulated widely that two people whose phases overlay into a complete circle are soulmates. Arithmetically it is one condition — the two elongations summing to a full turn, one waxing and one waning at mirror distances from new — and it is a real geometric relationship. It appears in no astrological text before this decade.
This tool computes it, names it, and says what it is. Refusing to compute a thing people came for would be precious; presenting a four-year-old internet format as ancient wisdom would be dishonest. Both are avoidable.
Why no birth time is asked for
The Moon covers about twelve degrees a day, so a calendar day spans roughly a quarter of a phase. For a birth in the middle of a phase the hour makes no difference at all; for one near a boundary it decides the answer. Rather than collect a birth time that most visitors do not have to hand, this tool computes noon UTC, says so on the result, and flags any date that lands close enough to a boundary for the neighbouring phase to be defensible.
If you do have an exact birth time and want the Moon placed to the arcminute — with its sign, its house and everything else — that is a full birth chart, and the method page says where this site stops.
How accurate this is
The Moon's position comes from the complete sixty-term lunar longitude series, which is accurate to about ten arcseconds — a six-hundredth of a degree. The Sun's is better than a hundredth of a degree. Both are computed in your browser from published astronomical series, not looked up in a shipped table, which is what makes it possible to check them: the site's own tests compare the results to real new and full moons rather than to themselves.