Moon Phase Calculator – Free Calculator

Understanding the moon phase calculator — concept and principle

The moon phase calculator estimates the Moon's age (days since the last new moon), the fraction of its disc that is lit, and the phase name for a given date. It helps you plan dark-sky observing or check the phase on any past or future date.

Count days since a known new moon; 27.6 of 29.5 days means a thin waning crescent.

How it is calculated

Convert the date to a Julian Date (JD) at 0h UTC using the Meeus algorithm.
Age = (JD − 2,451,550.26) mod 29.530588853. The reference JD 2,451,550.26 is the new moon of 6 January 2000, 18:14 UTC, and 29.530588853 days is the mean synodic month.
Illumination = (1 − cos(2π × age / 29.530588853)) / 2 × 100%.
The phase name comes from dividing the cycle into eight bands of about 3.69 days: new moon below 1.85 days, then waxing crescent, first quarter, waxing gibbous, full moon (12.92–16.61 days), waning gibbous, last quarter, waning crescent, and new moon again from 27.68 days.

The principle

A synodic month is the time from one new moon to the next. It is longer than the 27.3-day orbit relative to the stars because Earth also moves, so the Moon must travel further to line up with the Sun again. Counting whole synodic months from a known new moon tells you where in the cycle any date falls. The lit fraction follows from geometry: when the Sun–Moon angle seen from Earth is θ, the visible illuminated fraction is (1 − cos θ)/2, which is 0 at new moon, 50% at the quarters and 100% at full moon. The calculator assumes θ grows evenly with time.

Worked example

Input: 8 November 2026, so JD = 2,461,352.5 (0h UTC).
Days since the reference new moon: 2,461,352.5 − 2,451,550.26 = 9,802.24.
9,802.24 ÷ 29.530588853 = 331.94 cycles; 331 whole cycles are 9,774.62 days, leaving an age of 27.61508966 days.
Illumination = (1 − cos(2π × 27.615 / 29.5306)) / 2 = 4.1%.
Age 27.6 lies between 23.99 and 27.68, so the phase is waning crescent; the next mean new moon is about 1.9 days away.

Each point is the calculator re-run with only “Day” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Day	Moon age (days)
2	21.61508966
4	23.61508966
6	25.61508966
8	27.61508966
10	0.0845008042
12	2.084500804
16	6.084500804

How to read the result

An age near 0 or 29.5 means a new moon, the darkest skies for deep-sky observing. Around 7.4 days is first quarter (evening sky), 14.8 days is full moon (up all night) and 22.1 days is last quarter (morning sky). A waning crescent rises before dawn.

Common mistakes

Expecting the exact minute of new or full moon; the real Moon's orbit is elliptical, so actual phases can be several hours from the mean schedule.
Forgetting that the date is evaluated at 0h UTC, which is 9:00 in Korea.
Thinking the phase differs between countries; it is the same everywhere at the same instant, though the Southern Hemisphere sees the shape flipped.

Keep in mind: This is a mean-motion model with accuracy of about ±1 day. Use an almanac for eclipse timing, tides or religious calendars.

Frequently asked questions

Why does the Moon look full for two or three nights?

Near full moon the illumination changes slowly; it stays above about 95% for roughly two days on each side.

What is the difference between moon age and the lunar calendar date?

Lunar calendar days start counting from the new-moon day as day 1, so the calendar date is usually about one more than the age, and it is fixed per day rather than continuous.

Sources: J. Meeus, Astronomical Algorithms, 2nd ed., Willmann-Bell, 1998 (Chapters 7, 48 and 49) · NASA, Moon Phases (science.nasa.gov)

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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