About

The lunar synodic period is 29.53059 days, measured from one New Moon to the next. Miscounting the phase by even a single day shifts illumination by roughly 3.4%. This tool computes the Moon's age from a known New Moon epoch (January 6, 2000 at 18:14 UTC) and derives the phase angle φ to render the terminator line on a spherical projection. It does not use photographic textures or lookup tables. The illumination fraction f and terminator geometry are calculated from first principles for any date in history or the future.

The rendering approximates the Moon as a Lambertian sphere viewed from a fixed ecliptic perspective. It does not account for libration, parallax, or atmospheric effects. For agricultural, tidal, or religious calendar applications where precise phase boundaries matter, cross-reference with ephemeris data from the USNO or JPL Horizons. Pro tip: the eight traditional phase names use 45° boundaries on the phase angle, but the human eye struggles to distinguish a Waxing Crescent from a Waxing Gibbous near the quarter points.

Formulas

The Moon's age in days from a reference New Moon epoch is computed as:

age = ( JD_now − JD_epoch ) mod T_syn

where JD_now is the Julian Date of the target moment, JD_epoch = 2451550.26 is the Julian Date of the reference New Moon (2000-01-06 18:14 UTC), and T_syn = 29.53058770576 days is the mean synodic month.

The phase angle in radians:

φ = 2 π × ageT_syn

The illumination fraction visible from Earth:

f = 1 − cos(φ)2

For rendering the terminator on a circular disc of radius R, the terminator is drawn as an ellipse with semi-major axis R (vertical) and semi-minor axis:

t_x = R × |cos(φ)|

When φ < π (waxing), the right side is illuminated. When φ ≥ π (waning), the left side is illuminated. The terminator curve and the disc edge together define the shadow region, which is filled to produce the visible phase shape.

Reference Data

Phase Name	Phase Angle Range	Illumination	Moon Age (days)	Moonrise (approx.)	Moonset (approx.)	Visibility
New Moon	0° - 45°	0 - 2%	0 - 3.69	~06:00	~18:00	Not visible
Waxing Crescent	45° - 90°	2 - 50%	3.69 - 7.38	~09:00	~21:00	Afternoon & evening
First Quarter	90° - 135°	50%	7.38 - 11.07	~12:00	~00:00	Afternoon & first half of night
Waxing Gibbous	135° - 180°	50 - 100%	11.07 - 14.77	~15:00	~03:00	Late afternoon through most of night
Full Moon	180° - 225°	100%	14.77 - 18.46	~18:00	~06:00	All night
Waning Gibbous	225° - 270°	100 - 50%	18.46 - 22.15	~21:00	~09:00	Most of night & early morning
Last Quarter	270° - 315°	50%	22.15 - 25.84	~00:00	~12:00	Late night & morning
Waning Crescent	315° - 360°	50 - 0%	25.84 - 29.53	~03:00	~15:00	Pre-dawn & morning
Named Full Moons (Northern Hemisphere tradition)
Wolf Moon	January Full Moon		Named by Native American & Colonial traditions for howling wolves
Snow Moon	February Full Moon		Heaviest snowfall period in North America
Worm Moon	March Full Moon		Ground thaws, earthworm casts appear
Pink Moon	April Full Moon		Named for phlox subulata (moss pink) blooms
Flower Moon	May Full Moon		Widespread wildflower blooming
Strawberry Moon	June Full Moon		Strawberry harvesting season begins
Buck Moon	July Full Moon		Male deer begin growing new antlers
Sturgeon Moon	August Full Moon		Great Lakes sturgeon most readily caught
Harvest Moon	September/October Full Moon		Closest Full Moon to autumnal equinox; extra evening light for harvesting
Hunter’s Moon	October/November Full Moon		Fields cleared after harvest; prey visible under moonlight
Beaver Moon	November Full Moon		Time to set beaver traps before waters freeze
Cold Moon	December Full Moon		Onset of winter cold; longest nights of the year

Frequently Asked Questions

This tool uses the mean synodic period of 29.53059 days and a single reference epoch. The true lunar orbit is elliptical with variable angular velocity (anomalistic month ≈ 27.55455 days). Perturbations from the Sun, Earth's oblate shape, and other planets cause the actual synodic month to vary between roughly 29.27 and 29.83 days. For sub-1% accuracy, ephemeris-grade algorithms (like Jean Meeus's series expansions) are required. This tool's error is typically under 1 day of moon age, which translates to ≈3.4% illumination deviation.

The 360° cycle is divided into eight equal 45° sectors. New Moon occupies 0° - 45°, Waxing Crescent 45° - 90°, First Quarter 90° - 135°, and so on. This is a convention, not a physical boundary. The IAU does not formally standardize phase-name boundaries. Some sources use narrower windows (e.g., ±1 day) for the four principal phases and assign the remaining days to the intermediate phases.

No. The model treats the Moon as a smooth Lambertian sphere with no axial tilt relative to the observer. Real libration (up to ±7.9° in longitude and ±6.7° in latitude) causes the visible disc to wobble slightly, revealing about 59% of the surface over time. Earthshine (the faint illumination of the dark portion by sunlight reflected off Earth) is not rendered. Both effects are observational subtleties that do not change the primary phase shape.

No. Eclipses require the Moon to be near a node of its orbital plane (the ascending or descending point where the Moon's orbit crosses the ecliptic). This tool does not model orbital inclination (~5.145°) or nodal regression (~18.61 years). A Full Moon only produces a lunar eclipse when the Moon is within approximately ±6° of a node. Use dedicated eclipse catalogs like NASA's Five Millennium Canon for prediction.

From the Northern Hemisphere, the Moon is observed in the southern sky, and sunlight arrives from the west (right) during the waxing phases. In the Southern Hemisphere, the convention is reversed: the left side illuminates first. Near the equator, the terminator appears more horizontal. This tool uses the Northern Hemisphere convention. To mentally convert for the Southern Hemisphere, mirror the image horizontally.

The reference epoch is JD 2451550.26, corresponding to the New Moon of January 6, 2000 at 18:14 UTC. This date was chosen because it is a well-documented astronomical New Moon close to the J2000.0 standard epoch (January 1.5, 2000 TT). Using a nearby New Moon minimizes accumulated error from the mean synodic period approximation over short time spans.