About the Moon Phase Calculator
This tool works out where the Moon is in its roughly 29.5-day cycle for any date you pick, using the same reference-epoch method that powers most general-purpose moon phase tools. It reports the phase name (New Moon, Waxing Crescent, First Quarter, and so on), the percent of the visible disk that is lit, the Moon's age in days since the last new moon, and the calendar date of the next full moon.
The formula
The Moon completes one full cycle of phases — called a synodic month — in an average of 29.530588853 days. The calculator anchors that cycle to a known new moon that occurred on January 6, 2000, at 18:14 UTC. For your chosen date and hour, it:
- Converts the date and hour to a Julian Day number using the standard Gregorian-calendar formula.
- Subtracts the reference new moon's Julian Day to get the number of days elapsed, then divides by the synodic month length and keeps the remainder — this is the Moon's age in days (0 at new moon, up to about 29.53 just before the next new moon).
- Converts age to percent illumination with the standard circular-orbit approximation: illuminated fraction = (1 − cos(2π × age ÷ synodic month)) ÷ 2. That gives 0% at new moon, 50% at each quarter, and 100% at full moon.
- Maps the age to one of eight named phases by dividing the cycle into eight equal segments (each about 3.69 days), and finds the next full moon by measuring the distance forward to the point in the cycle where age equals half the synodic month (about 14.77 days).
Reading the phase names
The eight standard phases, in order, are New Moon, Waxing Crescent, First Quarter, Waxing Gibbous, Full Moon, Waning Gibbous, Last Quarter, and Waning Crescent, before the cycle returns to New Moon. "Waxing" means the illuminated portion is growing night to night; "waning" means it is shrinking. In the Northern Hemisphere the lit limb faces right while waxing and left while waning; from the Southern Hemisphere the sides are mirrored, which is why the hemisphere selector only changes that description, not the underlying math.
Assumptions and accuracy
This is a simplified astronomical model, not a precision ephemeris. It assumes a constant orbital speed and a fixed average synodic month, while the Moon's real orbit is elliptical and its actual speed varies through the month. In practice that keeps the phase name accurate to within about a day and illumination accurate to within a couple of percentage points — close enough for stargazing, tide-adjacent planning, or general reference, but not a substitute for a professional almanac when timing an eclipse or occultation matters.