Moon Phase Calculator

The calculator estimates phase from a fixed mean synodic month of 29.5305882 days and a reference new moon. It assigns the date to one of eight broad phase windows. It is not a lunar ephemeris and should not be used for exact full-moon, new-moon, rise, set, tide, or perigee timing.

New moon, waxing crescent, first quarter, waxing gibbous, full moon, waning gibbous, last quarter, and waning crescent. "Waxing" means the illuminated portion is growing (between new and full), and "waning" means it is shrinking (between full and the next new moon). Quarters are when exactly half the disk is illuminated, gibbous covers the broader-than-half phases, and crescent covers the narrower-than-half phases. The calculator picks one of the eight by which 1/8-of-a-cycle window the date lands in.

The synodic month, also called a lunation, is the average time between two new moons as seen from Earth, and it is 29.5305882 days. That is longer than the sidereal month (27.3 days, one orbit relative to the stars) because Earth itself moves around the Sun, so the Moon has to swing a bit farther to catch up to the same Sun-Earth-Moon alignment. Every phase prediction uses the synodic period: the moon's age in days is just (date minus last new moon) modulo 29.5306.

The fraction of the moon's Earth-facing disk that is lit by the Sun, expressed from 0% (new moon) to 100% (full moon). The formula is illumination = (1 - cos(2 pi phase)) / 2, where phase is the position in the synodic cycle (0 at new moon, 0.5 at full). A first or last quarter is exactly 50% illuminated. The percent does not change linearly with time: the moon races from new to half-lit in 7.4 days and from half-lit to full in another 7.4 days, but most of the visible change happens close to the half phases.

A supermoon requires a full moon near lunar perigee, but this calculator does not compute lunar distance or the exact full-moon instant. Its full-moon label covers a broad phase window, so a candidate flag is only a prompt to check an astronomical ephemeris.