Moon phase and illumination calculator

The Moon’s geocentric position comes from the main terms of the ELP-2000/82 lunar theory as tabulated by Meeus (chapter 47: 60 periodic terms each for longitude and distance and 60 for latitude), accurate to about 10″. The Sun uses Meeus’s solar coordinates. The elongation ψ is the angle between the Sun and Moon seen from Earth (cos ψ = cos β cos(λ − λ_☉)), the phase angle i follows from tan i = R sin ψ / (Δ − R cos ψ) with R and Δ the Sun’s and Moon’s distances, and the illuminated fraction is k = (1 + cos i) / 2 (chapter 48).

New moon, first quarter, full moon and last quarter are the instants when the Moon’s apparent longitude exceeds the Sun’s by 0°, 90°, 180° and 270°; the page solves for those instants directly, converting between Terrestrial Time and UTC with ΔT (from the leap-second table since 1972, and Espenak and Meeus’s polynomials otherwise). Within 12 hours of a principal phase the day is named after it; otherwise it is a waxing or waning crescent or gibbous Moon. Age is the time since the previous new moon.

Worked examples: Meeus’s example 47.a (12 April 1992, 0h TT) gives longitude 133.162655°, latitude −3.229126° and distance 368,409.7 km, and example 48.a gives an illuminated fraction of 0.6786, which this page reproduces. It finds the new moon of 8 April 2024 at 18:21 UTC and the full moon of 14 March 2025 at 06:55 UTC, the times the US Naval Observatory publishes.

Limits

Phase times are accurate to about a minute. Illumination is geocentric: from a particular place it differs by less than 0.1 percentage point. Moonrise and moonset are not calculated. The page opens on the current time and your device’s time zone.

References

• Meeus, J. (1998). Astronomical Algorithms, 2nd ed., chapters 47–49 (Willmann-Bell)
• US Naval Observatory: phases of the Moon
• NASA: Polynomial expressions for Delta T (Espenak and Meeus)
• IANA Time Zone Database