How is the moon phase calculated?

From the positions of the moon and sun. The elongation — the angle between them as seen from Earth — runs from 0° at new moon to 180° at full and back again. The illuminated fraction follows from the phase angle at the moon, giving k = (1 + cos i) ÷ 2. This page uses Meeus's lunar series for the moon's longitude, which is accurate to about a hundredth of a degree.

How long is a lunar cycle?

On average 29.530589 days, called the synodic month, but individual cycles vary between roughly 29.27 and 29.83 days. The variation comes from the moon's elliptical orbit — it moves faster when nearer Earth and slower when further away — combined with Earth's own motion around the sun. That half-day swing is why counting fixed 29.53-day steps drifts noticeably within a few years.

What is the moon's age?

The number of days since the last new moon, running from 0 to about 29.5. An age of about 7.4 days is first quarter, 14.8 is full and 22.1 is last quarter, though those figures shift by a few hours either way depending on where the moon is in its orbit. Age is a convenient shorthand, but the illuminated fraction is the more precise description of what you will actually see.

Why is the half moon called a quarter?

Because it marks a quarter of the way through the cycle, not a quarter of the disc. At first quarter the moon has completed one quarter of its journey from new moon to new moon, and half its visible face is lit. The name describes the position in the orbit, which is also why it appears at 90° elongation — exactly a quarter of the full 360° circuit.

Why is a crescent curved but a half moon straight?

Because the terminator is a circle seen at an angle. The line dividing lunar day from lunar night is a great circle on the moon's surface, and when you view a circle obliquely it projects as an ellipse. At the quarters you are looking straight along that circle's plane, so it projects as a straight line. Away from the quarters you see it tilted, so it curves — inward for a crescent, outward for a gibbous moon.

Does the moon phase look the same everywhere?

The phase is identical worldwide — everyone sees the same illuminated fraction at the same moment — but the orientation differs. From the northern hemisphere a waxing moon is lit on the right; from the southern it is lit on the left, because you are effectively viewing it upside down. Near the equator it can appear lit from below, which is why a waxing crescent there looks like a smile rather than a letter D.

Two definitions are in circulation. The seasonal one, which is older, is the third full moon in a season containing four. The monthly one, popularised by a magazine error in 1946, is the second full moon in a calendar month. The monthly kind happens because 29.53 days is shorter than most months, so roughly every two and a half years a month catches two full moons. February never can.

Why is there not an eclipse every month?

Because the moon's orbit is tilted about 5° to Earth's orbital plane, so at most new moons its shadow passes above or below Earth entirely, and at most full moons it passes above or below Earth's shadow. Eclipses need the moon near one of the two nodes where the orbits cross, at the same time as new or full. That alignment recurs in a pattern known as the saros, roughly every 18 years and 11 days.

How accurate are these times?

The illuminated fraction is good to well under a percent, and new and full moon times to within a few minutes. The main limit is the truncated series used for the moon's longitude — sixteen terms rather than the full sixty, which costs about a hundredth of a degree. For any practical purpose, including photography, gardening or knowing when the moon will be bright, that is far more precision than needed.

Moon Phase Calculator

Find the moon's phase for any date — the illuminated fraction, its age in days since the last new moon, and when the next new and full moons fall. The disc on the right is drawn to match, so you see the moon as it actually appears rather than a generic icon, and you can play the whole cycle through ...

PICK A DATE

DATE

phases are computed for noon Universal Time on this date

JUMP TO

PHASE

WAXING GIBBOUS

ILLUMINATED

77.9%

AGE

10.09 d

ELONGATION

123.7°

Waxing — growing towards full, and lit on the right as seen from the northern hemisphere.

Next new moon

Aug 12, 2026

at (UT)

17:36

Next full moon

Jul 29, 2026

at (UT)

14:38

This cycle

29.328 days

Days to next new

19.23 d

This cycle runs 29.33 days, not 29.53. The average is 29.53, but the moon travels faster near perigee and slower near apogee, so individual cycles range from about 29.3 to 29.8 days. A calculator that just counts 29.53-day steps from a reference new moon drifts by up to 21 hours — which is why the position is computed properly here instead.

WATCH THE CYCLE

newfirst quarterfulllast quarternew

The curved edge is a circle seen edge-on. The terminator — the line between lit and unlit — is the moon's day-night boundary viewed at an angle, so it projects as an ellipse. At the quarters that ellipse collapses to a straight line, which is why a half moon has a dead straight edge while a crescent and a gibbous moon both curve.

Southern hemisphere observers see this mirrored. From Australia or Chile a waxing moon is lit on the left, because you are effectively standing upside down relative to a northern observer. Near the equator it can appear lit from below entirely, which is why a waxing crescent there looks like a smile rather than a letter D.

Created with❤️byeaglecalculator.com

HOW TO USE

1
Pick a date. The phase is computed for noon Universal Time on that day, which is the usual convention since the moon's appearance changes only slightly over a few hours.
2
Read the phase name, the illuminated percentage and the moon's age — the number of days since the last new moon. The elongation is the angle between the moon and sun as seen from Earth, running from 0° at new to 180° at full.
3
Use the jump buttons to skip straight to the next new or full moon, or step forward a week or a month to see how the phase develops.
4
Press play to run the whole cycle, or drag the slider to any point in the lunation. The strip below shows the entire cycle at a glance, with a gold ring marking where your date falls.

THE NUMBERS BEHIND IT

Illuminated fractionk = (1 + cos i) / 2

Phase anglei, Sun–Moon–Earth

Elongationλ_moon − λ_sun

Mean synodic month29.530589 days

Actual range29.27 to 29.83 days

Sidereal month27.321661 days

Terminator semi-axisr · |2k − 1|

Waxingelongation below 180°

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Last updated: July 29, 2026 · Meeus lunar algorithm · Eagle-eyed accuracy for every calculation.