Moon Phases Explained: The 8 Lunar Phases
Why does the Moon have phases? Learn the 8 lunar phases, the 29.5-day synodic month and why phases are not caused by Earth’s shadow — with a diagram.
The idea behind it
The Sun lights half of the Moon. As the Moon orbits Earth, our viewing angle changes, revealing different fractions of that sunlit half. The repeating phase cycle is a synodic month.
The relationship to remember
(1 − cos(2π × 7.38 / 29.53059)) / 2 = 50% illuminated.
Make your own discovery
Slide from new Moon to full Moon. Watch the bright portion grow, then shrink during the second half of the cycle.
Open the Moon Phases Simulator — Interactive Lunar Cycle ↗Key formulas
| Quantity | Formula | Note or example |
|---|---|---|
| Illuminated fraction | k = (1 − cos(2π × age / 29.53)) / 2 | age in days since new Moon |
| Synodic month (phase cycle) | 29.53 days | New Moon to new Moon |
| Sidereal month (one orbit) | 27.32 days | Measured against the stars |
Worked examples
Each row uses one of this lab’s presets and the same model as the interactive tool.
| Example | Illuminated | Lunar age | Phase |
|---|---|---|---|
| New Moon | 0% | 0 days | New Moon |
| First quarter | 50% | 7.38 days | First quarter |
| Full Moon | 100% | 14.77 days | Full Moon |
| Last quarter | 50% | 22.15 days | Last quarter |
What this model leaves out
A mean 29.53059-day cycle, not a precision lunar ephemeris. Date estimates can differ from the actual phase by about a day. The diagram uses a conventional northern-hemisphere orientation; the apparent tilt depends on location and time.
Check your understanding
Are phases caused by Earth’s shadow?
No. Ordinary phases are changing views of the sunlit half of the Moon. Earth’s shadow causes a lunar eclipse.
Why is the phase month longer than the orbit?
While the Moon orbits, Earth moves around the Sun. The Moon needs extra time to return to the same alignment with the Sun.
What are the 8 phases of the Moon?
New Moon, waxing crescent, first quarter, waxing gibbous, full Moon, waning gibbous, last (third) quarter, and waning crescent. The full cycle takes about 29.5 days.
Continue with the formula reference or test yourself in space practice.