How is the phase computed, and how accurate is it?

The Moon's apparent longitude, latitude and distance come from the truncated ELP-2000/82 series in Meeus chapter 47 (about 60 terms each); the Sun uses the chapter 25 low-precision solution. Their separation gives the elongation ψ, then tan i = R sin ψ / (Δ − R cos ψ) gives the phase angle and the illuminated fraction is k = (1 + cos i)/2. The Moon's position is good to about 10″, so the fraction is far better than 0.1%. Times of the principal phases use the dedicated chapter 49 series: for example full moon 2025-01-13 22:27 UTC and new moon 2025-01-29 12:36 UTC, matching NASA to the minute.

What is the Moon's age, and why isn't full moon always at day 15?

Age is the time since the last new moon. A synodic month averages 29.53 days, but the orbit is elliptical: the Moon moves faster near perigee and slower near apogee. So the time from new to full varies between about 13.9 and 15.6 days, which is also why the Chinese lunar month's 15th day is not always the roundest.

Why does the lit side of the Moon point in different directions?

The bright limb always faces the Sun. Astronomers describe it with the position angle χ measured from celestial north through east. From the ground you also need the parallactic angle q, the tilt of celestial north relative to the zenith. An evening crescent in the west has its lit side toward the set Sun at lower right; a morning crescent in the east points lower left. Observers in the Southern Hemisphere see the Moon upside down compared with the north. Turn on the zenith-up view to see this.

It isn't a formal astronomical term. It usually means a full (or new) moon close to perigee. This tool flags one when the centre-to-centre distance is under 360,000 km, a common definition. Such a full moon looks about 14% wider and 30% brighter than one at apogee, though the difference is hard to notice by eye. The farthest full moons are called micromoons.

How are moonrise and moonset found, and why might they differ from an observatory's?

The Moon's geocentric altitude is computed every 10 minutes and compared with h₀ = 0.7275π − 34′, where π is the horizontal parallax; this accounts for refraction and the Moon's semi-diameter. Sign changes are refined by bisection, and transit is where the hour angle is zero. These are sea-level, flat-horizon values that usually agree with published tables to a minute or two. Buildings, hills or altitude change what you actually see. Because the Moon rises about 50 minutes later each day, some days have no moonrise or no moonset.

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🌔Moon Phase Calculator - Moon Phase Today, Moonrise, Full Moon Dates

This moon phase calculator works out the Moon's phase for any moment using the lunar and solar series from Meeus' Astronomical Algorithms: illuminated fraction, age, elongation, Earth–Moon distance and apparent size. It draws the Moon with its bright limb pointing the right way for your location, shows a month calendar of phases with the exact times of new, first quarter, full and last quarter, and gives moonrise, transit and moonset for cities such as Beijing, Hong Kong, Tokyo, London, New York and Sydney.

Free · No sign-up · Runs in your browserLast updated: 2026-10-29

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How to use Moon Phase Calculator

1Pick a date, time and location; the time zone follows the city (you can change it)
2Read the Moon image and results: phase name, illumination, age, distance and where the Moon is between perigee and apogee
3Drag the time scrubber or press Play to watch the phase change over a month
4Click any day in the phase calendar, and check the upcoming full and new moons, with supermoons flagged

FAQ

How is the phase computed, and how accurate is it?: The Moon's apparent longitude, latitude and distance come from the truncated ELP-2000/82 series in Meeus chapter 47 (about 60 terms each); the Sun uses the chapter 25 low-precision solution. Their separation gives the elongation ψ, then tan i = R sin ψ / (Δ − R cos ψ) gives the phase angle and the illuminated fraction is k = (1 + cos i)/2. The Moon's position is good to about 10″, so the fraction is far better than 0.1%. Times of the principal phases use the dedicated chapter 49 series: for example full moon 2025-01-13 22:27 UTC and new moon 2025-01-29 12:36 UTC, matching NASA to the minute.
What is the Moon's age, and why isn't full moon always at day 15?: Age is the time since the last new moon. A synodic month averages 29.53 days, but the orbit is elliptical: the Moon moves faster near perigee and slower near apogee. So the time from new to full varies between about 13.9 and 15.6 days, which is also why the Chinese lunar month's 15th day is not always the roundest.
Why does the lit side of the Moon point in different directions?: The bright limb always faces the Sun. Astronomers describe it with the position angle χ measured from celestial north through east. From the ground you also need the parallactic angle q, the tilt of celestial north relative to the zenith. An evening crescent in the west has its lit side toward the set Sun at lower right; a morning crescent in the east points lower left. Observers in the Southern Hemisphere see the Moon upside down compared with the north. Turn on the zenith-up view to see this.
What is a supermoon?: It isn't a formal astronomical term. It usually means a full (or new) moon close to perigee. This tool flags one when the centre-to-centre distance is under 360,000 km, a common definition. Such a full moon looks about 14% wider and 30% brighter than one at apogee, though the difference is hard to notice by eye. The farthest full moons are called micromoons.
How are moonrise and moonset found, and why might they differ from an observatory's?: The Moon's geocentric altitude is computed every 10 minutes and compared with h₀ = 0.7275π − 34′, where π is the horizontal parallax; this accounts for refraction and the Moon's semi-diameter. Sign changes are refined by bisection, and transit is where the hour angle is zero. These are sea-level, flat-horizon values that usually agree with published tables to a minute or two. Buildings, hills or altitude change what you actually see. Because the Moon rises about 50 minutes later each day, some days have no moonrise or no moonset.

Features

Meeus chapters 47 and 49: phase times usually within a minute of NASA's
Bright limb drawn at its true position angle, zenith-up or north-up
Month calendar with daily Moon icons, illumination, perigee and apogee
Moonrise, transit and moonset times and azimuths for nine cities
Upcoming principal phases with supermoon and micromoon labels
Chinese lunar date with a link to the full calendar

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