How Moon phase angle and illumination are calculated

Phase angle and illumination answer related questions, but they are not duplicate names for one number. The calculator reports both so a result preserves the Moon's position within the lunation and the fraction of its apparent disc that is sunlit from the viewing geometry.

The input is an instant, not a date label. A local civil time is resolved with its IANA time zone and converted to UTC before the astronomical state is evaluated. Two users who submit equivalent instants receive the same physical state even when their local dates differ.

Physical lunar phase wheel with a photographed Moon and engraved angle scale

Phase angle tracks position through the cycle

Phase angle is the difference in geocentric ecliptic longitude between the Moon and Sun, normalized through 360 degrees. The principal targets are 0 degrees for new Moon, 90 for first quarter, 180 for full Moon, and 270 for last quarter. Values between those targets remain continuous; a familiar phase name is a readable category.

Waxing and waning therefore come from direction within the cycle, not from whether the illumination happens to be above a chosen percentage. Before 180 degrees the reported state is waxing; after 180 degrees it is waning. Near the wrap from 360 back to 0, the continuous geometry also explains why two very thin crescents can have similarly small illumination while lying on opposite sides of new Moon.

Illumination measures the lit apparent disc

Illuminated fraction is the fraction of the Moon's apparent disc receiving sunlight as seen from Earth. It is displayed as a percentage. Zero and one are limiting ideas for new and full geometry; an evaluated instant normally falls near rather than exactly on a rounded display boundary.

Illumination is calculated independently of the displayed phase name. A label covers a range, whereas the exact state continues to change within that range.

Worked example

Worked exact-instant example

For 26 August 2026 at 12:00 UTC, the Moon Phase Calculator returns:

Phase angle: 160.5012°
Illuminated fraction: 97.13%
Display state: waxing Full Moon band
Next principal phase: full Moon at 28 August 2026, 04:19 UTC

The Moon is highly illuminated but has not yet reached the 180-degree full-Moon point. Calling the instant simply “97% full” would lose both its waxing direction and its position relative to the next principal phase.

Read before comparing

Reference conditions

Phase and illumination use an Earth-centred frame; horizon position uses an observer-centred frame.
Displayed decimals are rounded for comparison, while observing conditions vary by place and time.
Phase names are category bands. Use the numeric angle and adjacent event timestamps when the boundary matters.

Next step

Use the working calculator

Calculate another exact instant with the same reference frame and conventions described on this working sheet.

Open Moon Phase Calculator