Moon Phase Software

Tools & method

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.

Phase angle tracks position through the cycle

The phase value used by this site 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 retain their numeric precision; a familiar phase name is assigned only as 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 modeled fraction of the Moon's apparent disc receiving sunlight as seen from Earth. The result is displayed as a percentage for interpretation, while the calculation retains a fraction internally. Zero and one are limiting ideas for new and full geometry; a real evaluated instant normally falls near rather than exactly on a rounded display boundary.

The site takes illumination from the astronomical engine's lunar illumination calculation. It does not infer the percentage from the displayed phase name, and it does not reverse a rounded percentage into an event time. That distinction matters because a label covers a range, whereas the exact state continues to change within that range.

Worked exact-instant example

For 26 August 2026 at 12:00 UTC, the same production calculation used by 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 searched 180-degree full-Moon event. Calling the instant simply “97% full” would lose both its waxing direction and its position relative to the next principal phase.

Calculation limits

Use the working calculator

Open the Moon Phase Calculator to calculate another exact instant with the same production logic. The calculator accepts the relevant input and keeps result state on its single canonical tool page.