astronomylabFor teachers
The Moon changes. The reason doesn’t.

Moon phase explorer

Interactive Moon phases simulation: slide through the 29.5-day lunar cycle or pick a date to see the phase, illumination and why the Moon changes shape.

Moon phase explorerInteractive model
First quarter
Illuminated50%
Lunar age7.38 days
PhaseFirst quarter

Your experiment

(1 − cos(2π × 7.38 / 29.53059)) / 2 = 50% illuminated.

How it works

Illuminated fraction = (1 − cos(2π × age / 29.53059)) / 2

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.

Moon Phases Explained: The 8 Lunar Phases ↗

About this model
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.

Key formulas

QuantityFormulaNote or example
Illuminated fractionk = (1 − cos(2π × age / 29.53)) / 2age in days since new Moon
Synodic month (phase cycle)29.53 daysNew Moon to new Moon
Sidereal month (one orbit)27.32 daysMeasured against the stars

Worked examples

Each row uses one of this lab’s presets and the same model as the interactive tool.

ExampleIlluminatedLunar agePhase
New Moon0%0 daysNew Moon
First quarter50%7.38 daysFirst quarter
Full Moon100%14.77 daysFull Moon
Last quarter50%22.15 daysLast quarter
Keep wondering

Moon phase explorer: common questions

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.

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