A moon phase calculator tells you what the moon looks like on a given night, and the honest version of that question is astronomical rather than arithmetic. The lunar cycle averages 29.53 days, but no individual cycle is that length; they run from roughly 29.27 to 29.83 days because the moon's orbit is elliptical and the Earth's orbit around the sun is too. A calculator that simply takes the number of days since a known new moon and divides by 29.53 will drift by most of a day within a few years. This one does not work that way.
Arb Digital publishes this as part of a free tools library. It computes the ecliptic longitudes of the sun and the moon from standard periodic series, takes the angle between them, and derives the phase and the illuminated fraction from that angle directly. The next new and full moon are then found by searching forward for the exact instants when that angle passes through zero and 180 degrees. The method, its sources and its accuracy are set out below, because a moon calculator that will not say how it works is not worth trusting.
What This Moon Phase Calculator Does
Enter a date, a time and your UTC offset. The tool returns the named phase, the percentage of the visible disc that is sunlit, the moon's age in days since the last new moon, and the dates and times of the next new and full moon. The bars show the lit and dark fractions of the disc.
The hemisphere selector does not change any number. It changes the description of what you will see, because the moon appears rotated for observers in the southern hemisphere: a waxing crescent is lit on the right-hand limb from London and on the left-hand limb from Sydney. Near the equator the terminator often looks close to horizontal, which is why a crescent there is sometimes described as a smile.
There is no live tool on this site that this overlaps with. The nearest neighbours are date tools — the add days to date calculator, the date difference calculator and the day of week calculator — and all three do calendar arithmetic on a fixed civil calendar. This page does orbital mechanics, and the distinction matters precisely because the lunar month is not a fixed number of days.
How to Use It
- Set the date. It defaults to today. Any date across several centuries either side of the present will give a sensible answer.
- Set the time and your UTC offset. The phase changes measurably within a day — around ten per cent of illumination near the quarters — so the hour matters if you are close to a quarter or a full moon.
- Choose your hemisphere. This adjusts the description of which limb is lit rather than the phase itself.
- Read the illumination, not just the name. "Waxing gibbous" spans everything from 50 to 100 per cent lit; the percentage is the useful number.
- Use the next new and full dates for planning. New moon for astrophotography and stargazing, full moon for night visibility and for the largest tidal ranges.
The Formula / How It's Calculated
The phase of the moon is determined by one angle: the elongation, meaning the difference in ecliptic longitude between the moon and the sun as seen from Earth. At zero degrees the moon is new, at 180 degrees it is full, and the illuminated fraction of the disc follows directly:
k = (1 − cos θ) ÷ 2, where θ is the elongation in degrees.
Getting θ right is the whole job. The calculation converts the date to a Julian day number, forms the time argument T in Julian centuries from J2000.0 — that is 1 January 2000 at 12:00 terrestrial time, Julian day 2451545.0, the standard epoch used throughout modern astronomy. From T it evaluates the mean longitude, mean elongation, mean anomalies and argument of latitude of the moon, and the mean longitude and anomaly of the sun, then applies the leading periodic corrections from the standard lunar and solar series. Subtracting the two apparent longitudes gives θ.
Worked check. The dominant correction to the moon's longitude is the equation of the centre, 6.289 degrees times the sine of the moon's mean anomaly, which arises because the lunar orbit has an eccentricity of about 0.055. That single term can shift the moon by more than six degrees from its mean position, which is more than half a day of phase. The next term, evection at 1.274 degrees, and variation at 0.658 degrees, account for most of the remainder. A calculator that ignores these — which is what a 29.53-day modulus does — inherits their full error.
The moon's age is reported as θ divided by 360 and multiplied by the mean synodic month of 29.530588 days. That is a presentational convenience rather than an independent measurement, and it is why age is the least precise figure on this page. The next new and full moon are found by stepping forward and bisecting on the instant θ crosses zero or 180 degrees, so those two figures come from the same series as the phase itself rather than from adding a fixed interval.
Accuracy, Stated Honestly
This is a truncated series, not a full ephemeris. Keeping the leading terms of the lunar longitude series gives a position good to roughly a tenth of a degree, which translates to an illuminated fraction accurate to well under one per cent and phase instants accurate to within a few minutes for most cycles, occasionally stretching towards a quarter of an hour. That is more than adequate for planning an observing night, a photograph or a tide-sensitive activity.
It is not adequate for anything requiring second-level precision, and it makes no attempt at parallax, so it does not tell you what the moon looks like from a specific point on the Earth's surface as opposed to from the Earth's centre. It also ignores the difference between terrestrial time and universal time, which is currently around seventy seconds. For authoritative phase times, the US Naval Observatory publishes dates of the primary phases of the moon for any year from 1700 to 2100, and those are the figures to cite if precision matters.
The synodic period used for the age figure, 29.530588 days, is the mean value; NASA's own moon phases explainer gives the same cycle as about 29.5 days and contrasts it with the 27.3-day orbital period, which is the distinction most people trip over.
Why the Sidereal and Synodic Months Differ
The moon takes 27.32 days to complete one orbit relative to the stars — the sidereal month. But the phase cycle takes 29.53 days, two days longer, and the reason is that the Earth has moved. While the moon completes an orbit, the Earth advances about 27 degrees around the sun, so the moon has to travel a further 27 degrees or so to line up with the sun again. That extra distance takes roughly two extra days.
This is the single most useful fact about lunar timing and it explains several things at once. It is why the moon rises about fifty minutes later each night rather than an hour. It is why a lunar calendar of twelve months runs about eleven days short of a solar year, which is why Ramadan moves through the seasons and why the Hebrew calendar inserts leap months. And it is why the moon is never in exactly the same place at the same phase twice.
The variation around that average is large enough to notice. Because the lunar orbit is elliptical, the moon moves faster near perigee and slower near apogee, so consecutive new moons can fall more than half a day either side of the mean.
Reading the Phase in the Sky
Phase and time of day are locked together, which is more useful than it sounds. A new moon rises and sets with the sun, so it is never visible. A first quarter moon rises around noon, is highest around sunset, and sets around midnight — so an evening moon that is half lit is a first quarter. A full moon rises at sunset and sets at sunrise, opposite the sun all night. A last quarter rises around midnight and is highest around dawn, which is why a half moon seen in the morning sky is a last quarter, not a first.
The waxing and waning distinction is easy to get right once you know where to look. In the northern hemisphere the moon is lit on the right as it waxes and on the left as it wanes; south of the equator it is the reverse. If you see a crescent in the western sky after sunset it is waxing; a crescent in the eastern sky before dawn is waning. No calculator needed, though the numbers here will confirm it.
Earthshine is the bonus feature of a thin crescent. The dark portion of the disc is faintly visible because it is lit by sunlight reflected off the Earth, and it is brightest within a few days of new moon when the Earth as seen from the moon is close to full. That is the best time to photograph the whole disc in one exposure.
What Phase Actually Predicts
Tides are the strongest real effect. Spring tides — the largest range between high and low water — occur near new and full moon, when the sun and moon pull along the same line. Neap tides, with the smallest range, occur near the quarters. The effect lags the phase by a day or two in most locations because of the shape of the coastline, so a tide table beats a phase calculation for anything practical, but the phase tells you which week to look at.
Sky darkness is the other genuine one. Astronomers and astrophotographers plan around new moon because a bright moon washes out faint objects, and the useful window is roughly the ten days centred on new moon. Meteor showers are worth checking against phase for the same reason: a shower peaking at full moon will show a fraction of the meteors it would at new moon.
What phase does not predict is anything about weather, human behaviour or agriculture beyond the light available. If you are planning around dates rather than sky conditions, the days until date calculator will count down to a phase date from this page, and the leap year calculator settles the calendar side of long intervals. For orbital mechanics of a different kind, the Kepler's third law calculator relates orbital period to distance.
Arb Digital's free tools library covers science, date and measurement calculations, and our team is happy to hear what is missing from it.
Browse Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Treating the lunar month as exactly 29.53 days — individual cycles vary by more than half a day either side of that average.
- Confusing the sidereal and synodic months — the moon orbits in 27.32 days but the phase cycle takes 29.53, because the Earth moves too.
- Reading a phase name as a precise state — "waxing gibbous" covers everything from 50 to 100 per cent lit, so use the illumination figure.
- Forgetting the UTC offset — a phase instant given in universal time can fall on the previous or next calendar day where you are.
- Assuming the moon looks the same from both hemispheres — the disc appears rotated, so the lit limb swaps sides.
Related Free Tools From Arb Digital
Use the days until date calculator to count down to a new or full moon date, the add days to date calculator to step forward by a fixed interval, the date difference calculator for the gap between two dates, the day of week calculator for the weekday a phase falls on, and the Kepler's third law calculator for orbital period and distance relationships. The rest of the library is in the free online tools hub.
Frequently Asked Questions
It converts the date to a Julian day, evaluates standard periodic series for the ecliptic longitudes of the sun and moon, and takes the angle between them. The illuminated fraction is one minus the cosine of that angle, divided by two.
No. A fixed 29.53-day cycle drifts because real lunar months vary by more than half a day either side of the mean. This tool derives the phase from the sun and moon positions and finds the next new and full moon by searching for the exact crossing instants.
The truncated series gives lunar positions good to roughly a tenth of a degree, so the illuminated fraction is accurate to well under one per cent and phase instants to within minutes. For authoritative phase times, use the US Naval Observatory tables.
The moon completes an orbit relative to the stars in 27.32 days, but the Earth advances around the sun during that time, so the moon needs about two more days to line up with the sun again and repeat the same phase.
Not the phase itself, which is the same everywhere at a given instant. Location changes the orientation of the disc, so the lit limb appears on the opposite side from the southern hemisphere, and it changes the local time at which the moon rises and sets.
It is the elapsed time since the last new moon, quoted here as the elongation angle scaled by the mean synodic month of 29.530588 days. Because real cycles vary in length, age is the least precise figure on the page.
Around new moon, when there is no moonlight to wash out the sky. The useful window runs roughly ten days centred on the new moon date, which is why the next new moon figure is included here.
This tool computes geocentric positions from truncated astronomical series. It does not account for topocentric parallax or the small difference between terrestrial and universal time, and it is intended for planning and general interest rather than for navigation or precise timing.
