Moon Phase Calculator

The Moon's phases result from its orbital position relative to the Earth and Sun. As the Moon orbits Earth (approximately every 29.53 days), the angle between the Sun, Moon, and Earth changes, altering how much of the Moon's illuminated surface is visible from Earth. The synodic month (29.53 days) is the time between successive new moons. This differs from the sidereal month (27.32 days), which is the time for the Moon to complete one orbit relative to the stars. The difference arises because Earth has moved along its own orbit during the Moon's revolution, requiring the Moon to travel slightly more than 360 degrees to reach the same Sun-Moon-Earth alignment. The eight commonly recognized phases divide the lunar cycle into roughly equal segments. New Moon (day 0): the Moon is between Earth and Sun, invisible. Waxing Crescent (days 1-7): a sliver grows on the right. First Quarter (day 7.4): the right half is illuminated. Waxing Gibbous (days 7-15): more than half illuminated, growing. Full Moon (day 14.8): fully illuminated. Waning Gibbous (days 15-22): shrinking from the right. Last Quarter (day 22.1): left half illuminated. Waning Crescent (days 22-29): a sliver on the left fades. The illumination calculation uses a cosine function to approximate the percentage of the visible disk that is sunlit. At new moon (phase = 0), illumination is 0%. At full moon (phase = 0.5), illumination is 100%. This calculator provides an approximation. The actual lunar orbit is elliptical and affected by solar perturbations, so precise phase calculations require more complex astronomical algorithms. The approximation is typically accurate to within a day.