Moon Phase Calculator

Lunar guide

How moon phases work and how they are calculated

The moon does not produce its own light. What we see from Earth is sunlight reflecting off the lunar surface. As the moon orbits Earth, the angle between the Sun, Earth, and Moon changes continuously, which causes the lit portion of the moon visible from Earth to grow and shrink in a regular cycle. That cycle is what we call the lunar month.

The eight phases of the moon

The lunar cycle is divided into eight named phases based on how much of the moon is visibly illuminated and whether the lit area is growing or shrinking:

• New Moon (0%): The moon is between Earth and the Sun. The side facing us is entirely in shadow. This phase marks the start of a new lunar cycle.
• Waxing Crescent (1-49%): A thin sliver of the moon is lit on the right side. The lit area grows each night. Waxing means growing.
• First Quarter (50%): Exactly half of the moon is lit, on the right side. The moon is one quarter of the way through its cycle.
• Waxing Gibbous (51-99%): More than half the moon is lit and still growing. Just before full moon.
• Full Moon (100%): The moon is on the opposite side of Earth from the Sun. The entire face visible from Earth is illuminated.
• Waning Gibbous (99-51%): The lit area begins to shrink. Waning means decreasing.
• Last Quarter (50%): Half the moon is lit, now on the left side. Three quarters of the way through the cycle.
• Waning Crescent (49-1%): A thin sliver remains on the left side, shrinking toward the next new moon.

The synodic period

The time from one new moon to the next is called the synodic month or synodic period. It averages 29.530588853 days. This is longer than the moon's true orbital period around Earth (27.32 days, the sidereal month) because Earth itself is orbiting the Sun, so the moon has to travel a little extra to return to the same Sun-Earth-Moon alignment.

The synodic period is not exactly 29.5 days, which is why the calendar does not align neatly with lunar cycles. Over a year, there are approximately 12.37 synodic months, which is why some years have 13 full moons instead of 12.

How illumination percentage is calculated

The illumination fraction follows a cosine curve over the lunar cycle. At new moon, the phase angle is 0 and illumination is 0%. At full moon, the phase angle is 180 degrees (or 0.5 in normalized 0-1 terms) and illumination is 100%.

Where phase is a value from 0 to 1 representing how far through the current lunar cycle we are. The cosine function makes the transition between phases smooth and non-linear: the moon brightens and darkens faster near the quarters and more slowly near the new and full moon extremes.

How this calculator works

The calculator uses the Julian Day Number (JDN) system to convert any calendar date into a precise astronomical reference point. It then measures the elapsed time from a verified new moon epoch (January 6, 2000 at 18:14 UTC) and uses the synodic period to determine the current position in the lunar cycle.

This method is accurate to within about 1-2 hours for dates within a few centuries of the reference epoch. For precise lunar calendars used in navigation, agriculture, or religious observance, dedicated ephemeris tables with corrections for orbital eccentricity and other perturbations are used.

Why moon phases matter

The moon's gravitational pull drives the ocean tides, and the combined gravitational effect of the Sun and Moon produces the strongest tides (spring tides) around new and full moons, when all three bodies are aligned. Many cultures have tracked lunar cycles for agriculture, planting, harvesting, and religious calendars for thousands of years. The Islamic calendar, the Hebrew calendar, and the traditional Chinese calendar are all lunisolar or purely lunar systems.

In modern times, gardeners who follow biodynamic methods often plant or harvest by moon phase. Anglers reference the moon to predict fish feeding times. Photographers plan night shoots around the full moon or new moon depending on whether they want a moonlit landscape or dark skies for the Milky Way.

The blue moon

A blue moon is the second full moon in a single calendar month. Because the synodic month (29.53 days) is shorter than most calendar months (30-31 days), a month that begins with a full moon will end with one too. This happens roughly once every 2.5 years, giving rise to the phrase "once in a blue moon" for rare events. The moon itself does not actually turn blue, though rare atmospheric conditions caused by large wildfires or volcanic eruptions can scatter red wavelengths and make the moon appear bluish.

Disclaimer

Phase calculations are estimates based on a mean synodic period and a fixed reference new moon. They are accurate to within a few hours for most dates but do not account for the full complexity of lunar orbital mechanics, including eccentricity and perturbations from the Sun and other planets. For precise astronomical or navigation purposes, consult a dedicated ephemeris.