Moon Phase Calculator

Background.

Lunations are not all the same length. The one that began with the new moon of 15 June 2026 lasted 29.2842 days; the one that begins on 9 December 2026 runs 29.8142 days, almost 13 hours longer. The Moon's orbit is an ellipse, constantly tugged by the Sun, so the trip from one new moon to the next goes faster at some times than at others. NASA's Fred Espenak gives the mean synodic month as 29.53059 days and the extremes over five thousand years as 29.26574 and 29.84089 days.

That is why the phase here is worked out from the true instants of the new and full moons rather than by counting average months from a reference date. For any date and UTC time you get the phase name, the percentage of the disc that is lit, the Moon's age in days since the last new moon, the wait until the next full and new moons, and the length of the lunation you are in. The instants come from the periodic series in Jean Meeus's Astronomical Algorithms and agree with Espenak's published table of 2026 new and full moons to within about a minute and a half.

Phases are geocentric events. A full moon happens at one instant for the whole planet and only the local clock reading changes: the full moon of 26 October 2026, at 04:12 UTC, falls on the evening of 25 October in Honolulu and the morning of 26 October in Nairobi. Enter the time in UTC; converting your local time is the one step left to you.

Full moon and first quarter are strictly instants, but people use the words for a day or more around them. The names here come from the lit fraction, with bands of two percentage points around 0%, 50% and 100%: a naming convention, not astronomy.

What is moon phase calculator?

The Moon's phase is how much of its Earth-facing side is in sunlight, which is set by the phase angle i, the angle at the Moon between the directions to the Sun and to the Earth. The illuminated fraction of the disc is (1 + cos i) ⁄ 2: nothing at new moon, when i is close to 180°, half at i = 90°, and the whole disc at full moon, when i is close to 0°. The Moon's age is the time since the last new moon. Waxing means the lit part is growing, between new and full; waning means it is shrinking. Age and illumination only roughly track each other, because the Moon moves faster near perigee, its closest approach to Earth, than near apogee.

How to use this calculator.

1. 01Enter the date and the time in UTC, converting local time first: 21:00 in a zone three hours ahead of UTC is 18:00 UTC.
2. 02Leave TAI − UTC at 37 seconds for any date since 2017. It moves the results by seconds, so for older dates enter the value then in force only if you need the instants to the minute.
3. 03Read the phase name together with the illumination and the age. Near the quarters the lit fraction changes by about half a percentage point an hour, so the time of day matters.
4. 04Use the days to the next full and new moon for planning: add them to your date and time to get the instants in UTC.
5. 05Compare this lunation's length with 29.53 days to see how far the current month departs from the average.

The formula.

Two calculations run side by side. The first finds the instants of new and full moon. Chapter 49 of Meeus starts from a mean phase, JDE = 2451550.09766 + 29.530588861k plus tiny long-term terms, where k counts new moons from k = 0 on 6 January 2000 and k + ½ marks the full moon in between. Periodic corrections are then added, driven by the Sun's mean anomaly M, the Moon's mean anomaly M′, the Moon's argument of latitude F and the longitude of its node Ω. The largest, −0.40720 sin M′ days for a new moon, is worth up to 9.8 hours by itself; it is the Moon's elliptical orbit showing through. Terms are kept down to 0.00017 days, about 15 seconds, plus the largest planetary term. The series runs in Dynamical Time, so 32.184 seconds plus the leap-second count is subtracted to give UTC.

The second calculation gives the illumination at your instant. From the Moon's mean elongation D and the two anomalies (chapter 47), the low-precision phase angle of chapter 48 is i = 180° − D − 6.289° sin M′ + 2.100° sin M − 1.274° sin(2D − M′) − 0.658° sin 2D − 0.214° sin 2M′ − 0.110° sin D, and the lit fraction is (1 + cos i) ⁄ 2. Waxing or waning depends on whether your instant comes before or after this lunation's computed full moon. For dates well before 1972 the leap-second input cannot match the real clock difference, so the instants may drift by a minute or so, while illumination and phase name barely change.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Espenak, F. (NASA/GSFC), 'Eclipses and the Moon's Orbit' (last revised 2012 January 12). Verified by retrieval 2026-07-29 to state: mean synodic month 29.53059 days (29d 12h 44m 03s); the duration of the lunation varies over a range of 13h 48m 13s across 5000 years, with the shortest 29.26574 days and the longest 29.84089 days. This is the source of the variable-lunation argument on this page. Open access.
2. [2]Espenak, F., 'Six Millennium Catalog of Phases of the Moon' / 'Moon Phases: 2001 to 2100' (AstroPixels). Verified by retrieval 2026-07-29 for all twelve new moons and thirteen full moons of 2026 in Universal Time. This table is the empirical check: this calculator reproduces all twenty-five instants to within 1.525 minutes. Computed from a full lunar theory in the same family as the series implemented here, so it validates the truncation and the transcription rather than independently confirming the theory. Open access.
3. [3]Meeus, J. (1998). Astronomical Algorithms, 2nd edition, Willmann-Bell: chapter 47 (position of the Moon, mean elements), chapter 48 (illuminated fraction of the Moon's disk, low-precision phase angle) and chapter 49 (phases of the Moon). Source of every series coefficient implemented. Print / bibliographic reference.
4. [4]IERS Bulletin C, International Earth Rotation and Reference Systems Service. Verified by retrieval 2026-07-29: the difference between UTC and TAI is −37 seconds 'from 2017 January 1, 0h UTC, until further notice', and no leap second will be introduced at the end of December 2026. Source of the default leap-second input used to convert Dynamical Time to UTC. Open access.
5. [5]Chapront-Touzé, M. & Chapront, J. (1983), 'The lunar ephemeris ELP 2000', Astronomy & Astrophysics 124:50–62, and the later ELP2000-85 revision. The lunar theory from which the condensed series used here derive. Peer-reviewed; bibliographic reference.