Measure from the Sun to the Moon
In a geocentric tropical chart, take the Moon’s ecliptic longitude, subtract the Sun’s longitude, and wrap the result into one 360° cycle. A conjunction is near 0°, the waxing square near 90°, an opposition near 180°, and the waning square near 270°. The distinction between waxing and waning depends on the direction around the zodiac: a simple unsigned separation of 90° would lose it.
For a worked arithmetic example, put a hypothetical Sun at 20° Aries (20° absolute longitude) and a Moon at 5° Cancer (95°). The phase angle is 95°−20°=75°, which falls in the waxing crescent interval (45° to less than 90°). If the Moon instead stood at 5° Capricorn (275°), the angle would be 255°, a waning gibbous interval (225° to less than 270°). These numbers illustrate the rule; they are not a historical chart.
The eight intervals
| Angle | Phase | Geometric position |
|---|---|---|
| 0°–<45° | New Moon | Just past conjunction |
| 45°–<90° | Waxing Crescent | Moving toward the first square |
| 90°–<135° | First Quarter | Past the waxing square |
| 135°–<180° | Waxing Gibbous | Approaching opposition |
| 180°–<225° | Full Moon | Past opposition |
| 225°–<270° | Waning Gibbous | Moving toward the second square |
| 270°–<315° | Last Quarter | Past the waning square |
| 315°–<360° | Waning Crescent | Approaching the next conjunction |
What a missing hour changes
The Moon travels about a dozen zodiac degrees during a typical day, while the Sun moves roughly one. Near a 45° phase boundary, a date alone can therefore straddle two named intervals. A date-only tool should check the local day’s endpoints under the stated UTC offset and show both candidates if they differ. It should not give an exact birth angle for a person whose time is unknown. Daylight-saving changes within the day also require special care because one fixed offset cannot reproduce both sides of a clock shift.
Interpretation stays conditional
The eight labels are an astrological interpretive scheme. They can organize a reading of beginnings, culmination, and release, but an angular measurement does not establish a personality type or cause an event. The exact geometry and the meaning assigned to it are different kinds of claims. Compare the phase with the Moon sign, Sun sign, and chart aspects before using it as a theme, and keep approximate birth records marked as approximate.