Change year and month to display the lunar phase calendar in real time. Calculate moon age and phase from synodic month period to show new moon, full moon, and spring tide dates at a glance.
The moon changes shape a little every day, right? How does that work? It's not like the moon itself is turning on and off, is it?
🎓
Right, the moon doesn't emit its own light. It only reflects sunlight. The 'shape' of the moon changes depending on how much of the sunlit hemisphere is visible from Earth. At new moon, the moon is in the same direction as the sun, so the sunlit hemisphere faces away from Earth, making it appear dark. At full moon, the moon is opposite the sun (Earth between them), so the sunlit hemisphere faces us, making it appear round.
🙋
So what is 'lunar age'? People say things like 'today's lunar age is 14'.
🎓
Lunar age is the number of days since the last new moon: 0 for new moon, about 7.4 for first quarter (half moon), about 14.8 for full moon, about 22.1 for last quarter, and about 29.5 back to new moon. The synodic month cycle is about 29.530589 days, and this repetition creates the moon's phases. The old lunar calendar was based exactly on this cycle.
🙋
I often hear that spring tides occur during full moons. Why is that?
🎓
At new moon and full moon, the Earth, moon, and sun align in a straight line (syzygy). At these times, the moon's gravity and the sun's gravity combine in the same or opposite direction, maximizing tidal force—this is the spring tide. Conversely, at first and last quarter, the three bodies form a right angle, and the moon's and sun's gravity partially cancel out, causing neap tides. Coastal fishermen use this for planning their fishing seasons.
🙋
Why does the crescent moon swell from the right side day by day? Doesn't it ever swell from the left?
🎓
In the Northern Hemisphere, after a new moon, light always increases from the right (west) side—this is called 'waxing'. Because the moon orbits Earth counterclockwise, the sunlit portion increases sequentially from the right. In the Southern Hemisphere, it increases from the left. In Japan (Northern Hemisphere), the rule is 'swelling from the right toward full moon (waxing), waning from the left toward new moon (waning)'.
🙋
Is the lunar age calculation in this simulator accurate with the formula used?
🎓
This tool uses a simplified calculation based on the 'mean synodic month' (29.530589 days). The actual moon orbits in Kepler's elliptical orbit, moving faster near perigee and slower near apogee. Additionally, perturbations from the sun's gravity mean actual new/full moon times can deviate from the mean by several hours to about a day. For precise predictions, observatories use theories like ELP-2000 with hundreds of correction terms. For practical confirmation, refer to the National Astronomical Observatory of Japan's calendar calculation room (https://eco.mtk.nao.ac.jp/).
Frequently Asked Questions
What is a synodic month?
It is the period from one new moon to the next, approximately 29.530589 days (29 days, 12 hours, 44 minutes). It is the basis for one month in the lunar calendar (old calendar). Since it does not match the Gregorian calendar month (28–31 days), the dates of new moons and full moons shift each year and month.
Why do full moons and new moons cause spring tides?
At new moon and full moon, the Earth, moon, and sun align in a straight line. The gravitational forces of the moon and sun add up, maximizing tidal force (spring tide). At first and last quarter, the three bodies form a 90° angle, and the moon's and sun's gravity are orthogonal, partially canceling out, minimizing tidal force (neap tide). Spring tides peak about 2–3 days after new/full moon (tidal lag).
How many times can the moon be seen in a year?
Since the synodic month (29.53 days) is shorter than a calendar month, there are about 12.37 new moons and full moons per year. Most years have 12, but occasionally 13. A phenomenon with two full moons in one month is called a 'Blue Moon' (some months may have zero). A year with 13 months (adding a leap month in the old calendar) is set to correct this discrepancy.
How do moonrise and moonset times change?
Moonrise and moonset times are delayed by about 50 minutes each day. A new moon rises around sunrise (about 6:00 AM) and sets around sunset (about 6:00 PM). A first quarter moon rises around noon and sets around midnight. A full moon rises around sunset (about 6:00 PM) and sets around sunrise (about 6:00 AM). A last quarter moon rises around midnight and sets around noon.
What is the relationship between the old lunar calendar and lunar age?
The old calendar (in Japan, the 'lunisolar calendar') is a lunisolar calendar where the 1st day (tsuitachi) corresponds to a new moon, and the 15th day corresponds to a full moon. This is why the old calendar's '15th night' (harvest moon) falls on a full moon. However, since actual full moons can deviate from the mean, the 15th day of the old calendar is not always the roundest full moon day.
What is Moon Phase Calendar?
Moon Phase Calendar is a fundamental topic in engineering and applied physics. This interactive simulator lets you explore the key behaviors and relationships by directly manipulating parameters and observing real-time results.
By combining numerical computation with visual feedback, the simulator bridges the gap between abstract theory and physical intuition — making it an effective learning tool for students and a rapid-verification tool for practicing engineers.
Physical Model & Key Equations
The simulator is based on the governing equations behind Moon Phase Calendar Simulator. Understanding these equations is key to interpreting the results correctly.
$$$","$$$
Each parameter in the equations corresponds to a slider in the control panel. Moving a slider changes the equation's solution in real time, helping you build a direct connection between mathematical expressions and physical behavior.
Real-World Applications
Engineering Design: The concepts behind Moon Phase Calendar Simulator are applied across mechanical, structural, electrical, and fluid engineering disciplines. This tool provides a quick way to estimate design parameters and sensitivity before committing to full CAE analysis.
Education & Research: Widely used in engineering curricula to connect theory with numerical computation. Also serves as a first-pass validation tool in research settings.
CAE Workflow Integration: Before running finite element (FEM) or computational fluid dynamics (CFD) simulations, engineers use simplified models like this to establish physical scale, identify dominant parameters, and define realistic boundary conditions.
Common Misconceptions and Points of Caution
Model assumptions: The mathematical model used here relies on simplifying assumptions such as linearity, homogeneity, and isotropy. Always verify that your real system satisfies these assumptions before applying results directly to design decisions.
Units and scale: Many calculation errors arise from unit conversion mistakes or order-of-magnitude errors. Pay close attention to the units shown next to each parameter input.
Validating results: Always sanity-check simulator output against physical intuition or hand calculations. If a result seems unexpected, review your input parameters or verify with an independent method.