Free Online Moon Phase Calculator

About the Moon Phase Calculator

The Moon does not produce its own light. What we see is sunlight reflected from its rocky surface, and the changing shape in the sky is a consequence of geometry rather than a physical change in the Moon. As the Moon travels around Earth, the angle between the Sun, Earth, and Moon changes. When the Moon sits roughly between Earth and the Sun, its illuminated half faces away from us and we call it a new moon. Half a lunation later, Earth lies between the Sun and the Moon, the visible disc is fully lit, and we see a full moon. Crescent, gibbous, and quarter phases fill the stages in between.

How the calculation works

This page uses the open-source Astronomy Engine, which computes the Moon's geocentric position with a high-precision lunar theory. The phase angle is the difference between the Moon's apparent ecliptic longitude and the Sun's apparent ecliptic longitude as seen from Earth. A value near 0° corresponds to new moon, 90° to the first quarter, 180° to full moon, and 270° to the last quarter. The illuminated fraction follows the Lambertian relation (1 − cos θ) / 2, where θ is that phase angle. At 90° exactly half of the disc appears lit; at 180° the disc is complete; at 0° the near side is dark.

Moon age and the synodic month

Moon age is normally quoted as the number of days since the previous new moon. The mean interval between new moons, called the synodic month, is roughly 29.5306 days. The actual interval can differ by up to about seven hours because the Moon's orbital speed varies and the orbit is tilted relative to the ecliptic. The age shown here is derived from the phase angle and is therefore an approximation rather than an exact timestamp-based count. For observing planning, the phase name and illumination percentage are usually more useful than the age itself.

Phase names and what they mean

• New moon: the illuminated hemisphere faces away from Earth; the Moon is close to the Sun in the sky and is difficult to observe.
• Waxing crescent: a thin sliver grows on the right side in the northern hemisphere and on the left in the southern hemisphere.
• First quarter: half of the visible disc is lit and the Moon is roughly 90° east of the Sun.
• Waxing gibbous: more than half is illuminated but the disc is not yet complete.
• Full moon: the entire Earth-facing hemisphere is sunlit; the Moon rises near sunset and sets near sunrise.
• Waning gibbous, last quarter, and waning crescent: the lit portion shrinks until the next new moon.

Practical notes for observers

The best time to observe lunar craters is along the terminator, the boundary between light and shadow, where low Sun angles cast long shadows. A first quarter or last quarter moon often reveals more surface detail than a full moon, which can appear flat and excessively bright. Photography exposures change dramatically across the cycle: a full moon needs a much shorter exposure than a thin crescent. The calculator reports times in your own time zone so you can compare the result directly with a calendar or an observing session.

Frequently asked questions