CalculationTime

Moon Phase Calendar

A computed lunar calendar with phase discs, event timing, source-backed illumination and a CalculationTime clockface around the working tool.

Time Duration Calculator
August 2026
SunMonTueWedThuFriSat

Showing the sky as seen from the Southern Hemisphere, where the lit limb appears opposite to Northern views.

The formula

k = (1 - cos e) / 2

k is the illuminated fraction of the disc. e is the geocentric elongation: the Moon's ecliptic longitude minus the Sun's. At 0 degrees the Moon is new; at 180 degrees it is full.

Worked example - selected night

On Tue, 4 Aug 2026, the computed Moon-Sun elongation is 244 degrees. That gives 72% illumination and a waning gibbous.

Assumptions & limits

  • Principal phase times come from Astronomy Engine's Moon phase search, with event instants shown in your device's local timezone.
  • Daily discs use the geocentric Moon-Sun elongation at local noon, so they are calendar-scale phase views rather than a full sky-position simulation.
  • Illumination is the lit area of the disc, not perceived brightness.
  • The N/Eq/S toggle changes the displayed orientation, not the actual phase. Exact orientation in the sky still depends on time of night and observer latitude.

Sources

NASA Science - Moon phasesUSNO - Dates of primary phases of the MoonUSNO - Fraction of the Moon illuminatedAstronomy Engine - lunar phase search

Live math canvas

Your numbers, formula and explanation together

The moon calendar computes lunar phase, illuminated fraction and principal phase events from the selected month, date and viewing orientation.

Formula applied

The exact method behind this answer

CalculationTime keeps the method visible so the number can be checked instead of blindly trusted.

Illuminated fraction = (1 - cos(Moon-Sun elongation)) / 2. Phase labels come from the Moon-Sun angle and principal phase searches.
  1. Apply the methodIlluminated fraction = (1 - cos(Moon-Sun elongation)) / 2. Phase labels come from the Moon-Sun angle and principal phase searches.Phase, age and illuminationThe selected date determines Moon-Sun elongation, illumination and nearest principal phase context.

Your live breakdown

Current calculator context

This page keeps the active calculator, default worked example and method beside the tool so the answer is not separated from its arithmetic.

Calculator
Moon Phase Calendar
Computed lunar state
Phase, age and illumination
Current method
Illuminated fraction = (1 - cos(Moon-Sun elongation)) / 2. Phase labels come from the Moon-Sun angle and principal phase searches.

Resulting answer

Phase, age and illumination

The selected date determines Moon-Sun elongation, illumination and nearest principal phase context.

Calculator
Moon Phase Calendar
Computed lunar state
Phase, age and illumination
Current method
Illuminated fraction = (1 - cos(Moon-Sun elongation)) / 2. Phase labels come from the Moon-Sun angle and principal phase searches.

Assumptions used

What this answer assumes

These boundaries keep the calculation honest and make clear when a specialist rule set is needed.

  • Phase and illumination are calculated for astronomical geometry, then formatted for the visible calendar.
  • Northern, equatorial and Southern Hemisphere orientation changes the display, not the underlying lunar phase.
  • Local horizon, weather and observation conditions can change what a viewer actually sees.
  • Principal phase timings cite public astronomy sources and Astronomy Engine calculations.

Master’s Tip

How to use the result well

Master’s Tip: compare both the named phase and the illumination percentage. The visual phase name can stay the same while the lit fraction changes every night.

Printable record

What belongs in the saved calculation

A full Moon occurs when the Moon-Sun elongation is near 180 degrees, so the illuminated fraction approaches 100%. A new Moon is near 0 degrees, so illumination approaches 0%.

Calculator
Moon Phase Calendar
Computed lunar state
Phase, age and illumination
Current method
Illuminated fraction = (1 - cos(Moon-Sun elongation)) / 2. Phase labels come from the Moon-Sun angle and principal phase searches.

Embeddable calculator

Embed this calculator

Copy a clean iframe version with the required CalculationTime attribution link built in.

How it works

The calendar is built from elongation

The page computes the Moon's phase as ecliptic longitude relative to the Sun, then turns that angle into illuminated fraction. Principal phase times use Astronomy Engine's Moon phase search, while the visible method keeps the calendar checkable.

Phase

New, quarter and full labels are assigned from the computed Moon-Sun angle instead of a decorative icon set.

Orientation

The N/Eq/S toggle changes the display orientation so northern, equatorial and southern views can be compared.

Citation boundary

The page cites public astronomy explainers and phase data services, and names the engine used for event timing.

Citations

Source basis for the moon calendar

NASA ScienceMoon phase explanation, phase sequence and illuminated-side context.USNO Moon PhasesOfficial primary phase data service for new, quarter and full Moon dates.USNO Illuminated FractionFraction-illuminated reference for comparing phase and illumination.Astronomy EngineOpen-source Sun/Moon/planet calculation engine used for phase search timing.