Moon Phases Almanac

The short answer: read the light, then the clock

Two observations — the lit fraction and the hour you see the Moon — name any phase without an instrument.

Start with the disk. Fully lit means full; exactly half lit means a quarter; a thin sliver is a crescent; anything between half and full is a gibbous. In a normal waxing run the lit fraction climbs through five steps — 0%, about 25%, 50%, about 75%, 100% — and the waning half repeats them in mirror image.

Then read the geometry. A first quarter moon stands about 90° east of the Sun and is visible from about noon to midnight; a last quarter stands 90° west, shows the opposite half of the surface — the limb with the large craters such as Tycho — and belongs to the hours after midnight. Same 50%, different phase.

For a number rather than a name, the lit fraction is approximately (1 − cos elongation) / 2, where elongation is the Sun–Moon angle in the sky. That one formula converts any estimate of the angle into a percentage illumination.

The eight phases in order, and the days they fall on

The eight named phases divide the 29.53-day synodic month into steps of about 7.38 days.

Count from new moon: day 0 is new, day 7.38 is first quarter, day 14.77 is full, day 22.15 is last quarter, and day 29.53 is the next new. The four intermediate names — waxing crescent, waxing gibbous, waning gibbous, waning crescent — sit near the midpoints, around days 3.7, 11.1, 18.5 and 25.8.

The prefixes do real work: waxing means the lit fraction is growing toward full, waning that it is shrinking back toward new. A waxing and a waning crescent show the same roughly 25% of the disk — only the lit limb and the time of night tell them apart.

The phase-by-phase table with rise times and viewing windows lives on the companion page The Eight Moon Phases Explained (/moon-phases-explained); the condensed version appears in the table below.

A five-step field check, done in under a minute

Work the steps in order; each one names the mistake that most often breaks it.

The check works because the cycle is strict arithmetic wearing a visual costume: light, shape and schedule all derive from the same count of days since new moon, so any two of the three predict the third.

Run the steps on three consecutive evenings and the pattern shows itself — the lit fraction grows, the terminator creeps across the disk, and moonrise slips by roughly 50 minutes a day, all at the same pace.

If two steps disagree, trust the day-count in step five: it is the only one that cannot be fooled by haze, a low horizon or a rough guess at the lit fraction.

• Step 1 — Estimate the lit fraction to the nearest quarter: 0, 25, 50, 75 or 100%. Typical failure: calling a gibbous full — if any straight edge remains on the disk, it is not full yet.
• Step 2 — Decide waxing or waning from the lit limb: the waxing half of the cycle builds toward full, the waning half gives the light back. Typical failure: confusing the two crescents — both show about 25%, on opposite limbs.
• Step 3 — Check the hour against the phase's window: a half-moon visible from about noon to midnight is first quarter (90° east of the Sun); the same half-moon near dawn is last quarter. Typical failure: trusting yesterday's rise time — the Moon comes up about 50 minutes later each day.
• Step 4 — Convert the estimate into a cycle day: match it to 0, 3.7, 7.38, 11.1, 14.77, 18.5, 22.15 or 25.8 days after new moon. Typical failure: reading the percentage as a straight ramp — illumination follows a cosine and changes fastest near the quarters.
• Step 5 — Cross-check by counting from a known new moon: elapsed days modulo 29.53059 should land within about a day of your estimate. Typical failure: assuming a 30-day month — that shortcut drifts by nearly half a day every cycle.